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Similar Question 1
<p>Two trains leave Pittsburgh at the same time, one traveling east and the other traveling west. The eastbound train travels at 40 miles per hour, and the westbound train travels at 30 miles per hour. Let t represent the amount of time since their departure.</p><p>In how many hours will the trains be 245 miles apart?</p>
Similar Question 2
<p>Each gram of a mandarin orange has 0.26 mg of vitamin C and 0.13 mg of vitamin A. Each gram of tomato has 0.13 mg of vitamin C and 0.42 mg of vitamin A. How many grams of mandarin oranges and tomatoes have 13 mg of vitamin C and 20.7 mg of vitamin A? </p>
Similar Question 3
<p>Amy needs to make 10L of <code class='latex inline'>42\%</code> sulphuric acid solution. In the supply room, she finds bottles <code class='latex inline'>30\%</code> sulphuric acid solution and <code class='latex inline'>60\%</code> sulphuric acid solution. What volume of each solution should she mix in order to make the <code class='latex inline'>42\%</code> solution?</p>
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Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>A company excavated <code class='latex inline'>150</code> t of black coal that contained <code class='latex inline'>1.9\%</code> water and left it on the ground. After being rained on, the coal contained <code class='latex inline'>10\%</code> water. By what percent did the mass of the coal increase?</p>
<p>Evan spend a total of <code class='latex inline'>\$18</code> on gourmet jellybeans and chocolate-covered almonds. The jellybeans cost <code class='latex inline'>\$ 12</code>/kg. The almonds cost <code class='latex inline'>\$21</code>/kg.</p><p>a) Write an equation to represent Evan&#39;s purchases.</p><p>b) Isolate the variable for the quantity of jellybeans in your equation.</p><p>c) If Evan bought 250g of almonds, how many grams of jellybeans did he buy?</p><p>d) If Evan bought 100 g of almonds, how many grams of jellybeans did he buy?</p> <p>Happy Burger is made by combining cuts of pork and fat trim. The amount of fat in Happy Burger is limited by government regulations to no more than <code class='latex inline'>25\%</code>. A butcher has a supply of pork with fat content 20\%. He also has a supply of fat trim with fat content <code class='latex inline'>100\%</code>. He wants to make 20 kg of Happy Burger with a fat content of <code class='latex inline'>24\%</code>. How much pork and how much fat should he use?</p> <p>Each gram of a mandarin orange has 0.26 mg of vitamin C and 0.13 mg of vitamin A. Each gram of a tomato has 0.13 mg of vitamin C and 0.42 mg of vitamin A. How many grams of mandarin oranges and tomatoes have 13 mg of vitamin C and 20.7 mg of vitamin A? </p> <p>Each gram of a mandarin orange has 0.26 mg of vitamin C and 0.13 mg of vitamin A. Each gram of tomato has 0.13 mg of vitamin C and 0.42 mg of vitamin A. How many grams of mandarin oranges and tomatoes have 13 mg of vitamin C and 20.7 mg of vitamin A? </p> <p>Cookies Inc. sells peanut butter cookies for$6.50 per dozen and chocolate chip cookies for $9.00 per dozen. Yesterday, they sold 85 dozen more peanut butter cookies than chocolate chip cookies. The total sales for both types of cookies were$4055.50. Let p represent the number of dozens of peanut butter cookies sold.</p><p>How many dozen peanut butter cookies were sold?</p>
<p>Hakim invested <code class='latex inline'> \$15000 </code> . He put part of it in a term deposit that paid <code class='latex inline'> 4 \% </code> per annum, and the remainder in a treasury bill that paid <code class='latex inline'> 5 \% </code> per annum. After one year, the total interest was <code class='latex inline'> \$ 690 </code> . How much did Hakim invest at each rate?</p>
<p>A woodworking shop makes tables and chairs. To make a chair, 8 min is needed on the lathe and 8 min is needed on the sander. To make a table, 8 min is needed on the lathe and 20 min is needed on the sander. The lathe operator works 6 h/day, and the sander operator works 7 h/day. How many chairs and tables can they make in one day working at this capacity?</p>
<p>One type of antifreeze is 40% glycol, and another type of antifreeze is 60% glycol. How much of each kind should be used to make 100 gallons of antifreeze that is 48% glycol?</p>
<p>In Ms. Martinez’s science class, a test is worth three times as much as a quiz. If a student has test grades of 85 and 92 and quiz grades of 82, 75, and 95, what is the student’s average grade?</p>
<p>A cheetah is 300 feet from its prey. It starts to sprint toward its prey at 90 feet per second. At the same time, the prey starts to sprint at 70 feet per second. When will the cheetah catch its prey?</p><img src="/qimages/24558" />
<p>An express train travels 80 kilometers per hour from Ironton to Wildwood. A local train, traveling at 48 kilometers per hour, takes 2 hours longer for the same trip. How far apart are Ironton and Wildwood?</p>
<p>Cookies Inc. sells peanut butter cookies for $6.50 per dozen and chocolate chip cookies for$9.00 per dozen. Yesterday, they sold 85 dozen more peanut butter cookies than chocolate chip cookies. The total sales for both types of cookies were $4055.50. Let p represent the number of dozens of peanut butter cookies sold.</p><p>How many dozen chocolate chip cookies were sold?</p> <p>In 2000, the international price of gold was$270 per ounce, and the international price of silver was $5 per ounce. Suppose gold and silver were mixed to obtain 15 ounces of an alloy worth$164 per ounce. Let g represent the amount of gold used in the alloy.</p><p>Copy and complete the table representing the problem.</p><img src="/qimages/150160" />
<p>A student read a book in three days. During the first day the student read <code class='latex inline'>25\%</code> of the book. During the second day, the student read <code class='latex inline'>65\%</code> of the rest, and during the third day the students read 42 pages. How many pages were there in the book?</p>
<p>How many quarts of pure orange juice should Michael add to a 10% orange drink to create 6 quarts of a 40% orange juice mixture? Let <code class='latex inline'>p</code> represent the number of quarts of pure orange juice he should add to the orange drink.</p><p>Copy and complete the table representing the problem.</p><img src="/qimages/24552" />
<p>One lawn fertilizer is <code class='latex inline'>24\%</code> nitrogen, and another is <code class='latex inline'>12\%</code> nitrogen. How much of each fertilizer should be mixed to obtain 100 kg of fertilizer that is <code class='latex inline'>21 \%</code> nitrogen?</p>
<p>Hector is performing a chemistry experiment that requires 140 milliliters of a 30% copper sulfate solution. He has a 25% copper sulfate solution and a 60% copper sulfate solution. How many milliliters of each solution should he mix to obtain the needed solution?</p>
<p>How many quarts of pure orange juice should Michael add to a 10% orange drink to create 6 quarts of a 40% orange juice mixture? Let <code class='latex inline'>p</code> represent the number of quarts of pure orange juice he should add to the orange drink.</p><p>Write an equation to represent the problem.</p>
<p>A health-food company packs almond butter in jars. Some jars hold 250 g. Other jars hold 500 g. On Tuesday, the company packed 186.5 kg of almond butter in 511 jars. How many jars of each size did they pack?</p>
<p>An airplane flies 1000 miles due east in 2 hours and 1000 miles due south in 3 hours. What is the average speed of the airplane?</p>
<p><code class='latex inline'>3</code> kg of alloy that contained <code class='latex inline'>65\%</code> silver were melted together with <code class='latex inline'>2</code> kg of alloy that contained <code class='latex inline'>72\%</code> silver. Find the percentage of silver in the obtained alloy.</p>
<p>Refer to the graphic at the right. How much whipping cream and 2% milk should be mixed to obtain 35 gallons of milk with 4% butterfat?</p><img src="/qimages/24557" />
<p>Brand A fertilizer is <code class='latex inline'>32\%</code> phosphorus, while Brand B is <code class='latex inline'>18\%</code> phosphorus. How much of each must be used to produce 56 t of a <code class='latex inline'>24\%</code> mixture?</p>
<p>Jim researched these nutrition facts:</p> <ul> <li><code class='latex inline'>1g</code> of soy milk has <code class='latex inline'>0.005g</code> of carbo hydrates and <code class='latex inline'>0.030g</code> of protein.</li> <li><code class='latex inline'>1g</code> of vegetables has <code class='latex inline'>0.14 g</code> of carbohydrates and <code class='latex inline'>0.030 g</code> of protein.</li> </ul> <p>Jim wants his lunch to have <code class='latex inline'>50.000</code> g of carbohydrates and <code class='latex inline'>20.000</code> g of protein. How many grams of soy milk and vegetables does he need?</p>
<p>White vinegar is a solution of acetic acid in water. There are two strengths of white vinegar-a <code class='latex inline'> 5 \% </code> solution and a <code class='latex inline'> 10 \% </code> solution. How many millilitres of each solution must be mixed to make <code class='latex inline'> 50 \mathrm{~mL} </code> of a <code class='latex inline'> 9 \% </code> vinegar solution?</p>
<p>Sarah needs 20 g of 80% gold to make a pendant. She has some 85% gold and some 70% gold. from broken jewellery and wants to know how much of each she should use. Determine the quantity of each alloy that she should use.</p>
<p>A chemist mixes hydrochloric acid solution of <code class='latex inline'>50\%</code> strength and <code class='latex inline'>40\%</code> strength to get 500 L of hydrochloric acid solution of <code class='latex inline'>46\%</code> strength. How many litres of the <code class='latex inline'>50\%</code> solution are used?</p>
<p>A <code class='latex inline'>60\%</code> sulfuric acid solution will be mixed with a <code class='latex inline'>95\%</code> sulfuric acid solution to produce 2700 mL of a <code class='latex inline'>70\%</code> solution. How much of each is required?</p>
<p>Two trains leave Pittsburgh at the same time, one traveling east and the other traveling west. The eastbound train travels at 40 miles per hour, and the westbound train travels at 30 miles per hour. Let t represent the amount of time since their departure.</p><p>In how many hours will the trains be 245 miles apart?</p>
<p>In 2000, the international price of gold was $270 per ounce, and the international price of silver was$5 per ounce. Suppose gold and silver were mixed to obtain 15 ounces of an alloy worth $164 per ounce. Let g represent the amount of gold used in the alloy.</p><p>How much silver was used in the alloy?</p> <p>Sam is a jewellery artist. She needs to mix metals to make her products. Pure gold is 24-karat and is very soft. It is usually mixed with other metals such a silver to make it harder. Same has some 18-karat gold (18/24 pure gold) and some 9-kara gold (9/24 pure gold). what mass of each type of gold should she use to make 600 g of 15-karat gold?</p> <p>For his coffee shop, Abdul wants to make a mocha-java blend that will sell for <code class='latex inline'>\$18</code>/kg. The mocha coffee beans sell for <code class='latex inline'>\$20</code>/kg, and the java coffee beans sell for <code class='latex inline'>\$15</code>/kg. How many kilograms of each kind of coffee bean should he use to make <code class='latex inline'>50</code> kg of the mocha-java blend? </p>
<p>The Madison High School marching band sold gift wrap. The gift wrap in solid colors sold for $4.00 per roll, and the print gift wrap sold for$6.00 per roll. The total number of rolls sold was 480, and the total amount of money collected was $2340. How many rolls of each kind of gift wrap were sold?</p> <p>Two trains leave Pittsburgh at the same time, one traveling east and the other traveling west. The eastbound train travels at 40 miles per hour, and the westbound train travels at 30 miles per hour. Let t represent the amount of time since their departure.</p><p>Copy and complete the table representing the situation.</p><img src="/qimages/24556" /> <p>Amy needs to make 10L of <code class='latex inline'>42\%</code> sulphuric acid solution. In the supply room, she finds bottles <code class='latex inline'>30\%</code> sulphuric acid solution and <code class='latex inline'>60\%</code> sulphuric acid solution. What volume of each solution should she mix in order to make the <code class='latex inline'>42\%</code> solution?</p> <p>A lab technician needs to make 400 kg of <code class='latex inline'>51\%</code> alcohol solution by combining <code class='latex inline'>60\%</code> alcohol solution by mass and <code class='latex inline'>40\%</code> alcohol solution by mass. How many kilograms of the <code class='latex inline'>40\%</code> solution must be used?</p> <p>Milk and cream contain different percents of butterfat. How much <code class='latex inline'>3\%</code> milk needs to be mixed with how much <code class='latex inline'>15\%</code> cream to give <code class='latex inline'>20 L</code> of <code class='latex inline'>6\%</code> cream?</p> <p>Sea water contains <code class='latex inline'>5\%</code> salt. How many kilograms of distilled fresh water must be added of <code class='latex inline'>25</code> kg of sea water to decrease the concentration of salt to <code class='latex inline'>2\%</code>?</p> <p>Cookies Inc. sells peanut butter cookies for$6.50 per dozen and chocolate chip cookies for $9.00 per dozen. Yesterday, they sold 85 dozen more peanut butter cookies than chocolate chip cookies. The total sales for both types of cookies were$4055.50. Let p represent the number of dozens of peanut butter cookies sold.</p><p>Copy and complete the table representing the problem.</p><img src="/qimages/24554" />
<p>Many schools base a student’s grade point average, or GPA, on the student’s grade and the class credit rating. Brittany’s grade card for this semester is shown. Find Brittany’s GPA if a grade of A equals 4 and a B equals 3.</p><img src="/qimages/24553" />
<p>One type of fertilizer has 30% nitrogen and a second type has 15% nitrogen. If a farmer needs 600 kg Of fertilizer that is 20% nitrogen, how much of each type should the farmer mix together?</p>
<p>Ron needs 500 g of chocolate that is 86% cocoa for a truffle recipe. fl He has one kind of chocolate that is 99% cocoa and another kind that is 70% cocoa. How much of each kind of chocolate does he need to make the 86% cocoa blend? Round your answer to the nearest gram.</p>
<p>Two trains leave Pittsburgh at the same time, one traveling east and the other traveling west. The eastbound train travels at 40 miles per hour, and the westbound train travels at 30 miles per hour. Let t represent the amount of time since their departure.</p><p>Write an equation that could be used to determine when the trains will be 245 miles apart.</p>
<p> Mike has a bottle containing acid that is <code class='latex inline'>40\%</code> of 250 ml. To remove stains, the acid concentration needs to be <code class='latex inline'>60\%</code>. How much should Mike pour out his acid and replace with <code class='latex inline'>90\%</code> acid to get <code class='latex inline'>60\%</code> acid bottle?</p>
<p>Make a table that can be used to solve the following problem.</p><p>Lakeisha has $2.55 in dimes and quarters. She has 8 more dimes than quarters. How many quarters does she have?</p> <p>A chemist has one 30-L bottle of <code class='latex inline'>15\%</code> hydrochloric acid and one <code class='latex inline'>30-L</code>: bottle of <code class='latex inline'>90\%</code> hydrochloric acid. She mixes <code class='latex inline'>20 L</code> of <code class='latex inline'>60\%</code> hydrochloric acids and then puts <code class='latex inline'>5 L</code> of that solution back into the bottle containing the <code class='latex inline'>90\%</code> hydrochloric acid. How strong is the acid in that bottle now?</p><p><a href="https://youtu.be/A0iwZxy8DE4">Lecture video</a></p> <p>Wayne wants to use a few pieces of silver to make a bracelet. Some of the jewellery is <code class='latex inline'>80\%</code> silver, and the rest is <code class='latex inline'>66\%</code> silver. Wayne needs <code class='latex inline'>30.00g</code> of <code class='latex inline'>70\%</code> silver for the bracelet. How much of each alloy should he use?</p><p><a href="https://www.youtube.com/watch?v=SMfnqFG8xQ0&amp;feature=emb_logo">HINT 1</a> <a href="https://youtu.be/8CuPYmE9R3A">HINT 2</a></p> <p>An alloy of metals is 25% copper. Another alloy is 50% copper. How much of each alloy should be used to make 1000 grams of an alloy that is 45% copper?</p> <p>Two cyclists begin traveling in the same direction on the same bike path. One travels at 20 miles per hour, and the other travels at 14 miles per hour. When will the cyclists be 15 miles apart?</p> <p>A vinegar-water solution is used to wash windows. If 1200 L of a <code class='latex inline'>28\%</code> solution are required, how much of <code class='latex inline'>16\%</code> and <code class='latex inline'>36\%</code> solutions should be used?</p> <p>A sprinter has a bad start, and his opponent is able to start 1 second before him. If the sprinter averages 8.2 meters per second and his opponent averages 8 meters per second, will he be able to catch his opponent before the end of the 200-meter race? Explain.</p> <p>Todd drove from Boston to Cleveland, a distance of 616 miles. His breaks, gasoline, and food stops took 2 hours. If his trip took 16 hours altogether, what was his average speed?</p><p>A. 38.5 mph</p><p>B. 40 mph</p><p>C. 44mph</p><p>D. 47.5 mph</p> <p>The Nut Shoppe sells walnuts for$4.00 a pound and cashews for $7.00 a pound. How many pounds of cashews should be mixed with 10 pounds of walnuts to obtain a mixture that sells for$5.50 a pound?</p>
<p>Charley Baroni owns a specialty coffee store. He wants to create a special mix using two coffees, one priced at $6.40 per pound and the other priced at$7.28 per pound. How many pounds of the $7.28 coffee should he mix with 9 pounds of the$6.40 coffee to sell the mixture for $6.95 per pound?</p> <p>What volume, in millilitres, of a <code class='latex inline'> 60 \% </code> hydrochloric acid solution must be added to <code class='latex inline'> 100 \mathrm{~mL} </code> of a <code class='latex inline'> 30 \% </code> hydrochloric acid solution to make a <code class='latex inline'> 36 \% </code> hydrochloric acid solution?</p> <p>Lily needs 200 g of chocolate that is <code class='latex inline'>86\%</code> cocoa for a cake recipe. He has one kind of chocolate that is <code class='latex inline'>99\%</code> cocoa and another kind that is <code class='latex inline'>70\%</code> cocoa. How much of each kind of chocolate does he need to make the cake? Round your answer to the nearest gram.</p> <p>A car radiator has a capacity of 16 quarts and is filled with a 25% antifreeze solution. How much must be drained off and replaced with pure antifreeze to obtain a 40% antifreeze solution?</p> <p>Cookies Inc. sells peanut butter cookies for$6.50 per dozen and chocolate chip cookies for $9.00 per dozen. Yesterday, they sold 85 dozen more peanut butter cookies than chocolate chip cookies. The total sales for both types of cookies were$4055.50. Let p represent the number of dozens of peanut butter cookies sold.</p><p>Write an equation to represent the problem.</p>
<p>How many quarts of pure orange juice should Michael add to a 10% orange drink to create 6 quarts of a 40% orange juice mixture? Let <code class='latex inline'>p</code> represent the number of quarts of pure orange juice he should add to the orange drink.</p><p>How much pure orange juice should Michael use?</p>
<p>Isabel invested <code class='latex inline'> \$8000 </code> , part at <code class='latex inline'> 9 \% </code> per annum and the remainder at <code class='latex inline'> 4 \% </code> per annum. After one year, the total interest from these investments was <code class='latex inline'> \$ 420 </code> . How much did she invest at each rate?</p>
<p>Roaneeds 500 g of chocolate that is 86% cocoa for a truffle recipe. He has one kind of chocolate that is 99% cocoa and another kind that is 70% cocoa. </p><p>How much of each kind of chocolate does he need to make the 86% cocoa blend? Round your answer to the nearest gram.</p>
<p>One type of granola has 30% nuts, by mass. A second type of granola has 15% nuts. What mass of each type needs to be mixed to make 600 g of granola that will have 21% nuts?</p>
<p>A metal alloy is <code class='latex inline'>25\%</code> copper. Another metal alloy is <code class='latex inline'>50\%</code> copper. How much of each should be used to make 500 g of an alloy that is <code class='latex inline'>45\%</code> copper?</p>
<p>What volumes of 60% hydrochloric acid solution and 30% hydrochloric acid solution must be mixed to make 125 mL of 36% hydrochloric acid solution?</p>
<p>Each gram of a mandarin orange has 0.26 mg of vitamin C and 0.13 mg of vitamin A. Each gram of a tomato has 0.13 mg of vitamin C and 0.42 mg of vitamin A. How many grams of mandarin oranges and tomatoes have 13 mg of vitamin C and 20.7 mg of vitamin A? </p>
<p>Chemex Lab needs to make 500 L of a 34% acid solution for a customer. The lab has 25% and 50% acid solutions available to make the order. How many litres of each should be mixed to make the 34% solution?</p>
<p>A fishing trawler has radioed the Coast Guard for a helicopter to pick up an injured crew member. At the time of the emergency message, the trawler is 660 kilometers from the helicopter and heading toward it. The average speed of the trawler is 30 kilometers per hour, and the average speed of the helicopter is 300 kilometers per hour. How long will it take the helicopter to reach the trawler?</p>
<p>In 2000, the international price of gold was $270 per ounce, and the international price of silver was$5 per ounce. Suppose gold and silver were mixed to obtain 15 ounces of an alloy worth $164 per ounce. Let g represent the amount of gold used in the alloy.</p><p>Write an equation to represent the problem.</p> <p>In 2000, the international price of gold was$270 per ounce, and the international price of silver was $5 per ounce. Suppose gold and silver were mixed to obtain 15 ounces of an alloy worth$164 per ounce. Let g represent the amount of gold used in the alloy.</p><p>How much gold was used in the alloy?</p>
<p>Chemex Lab needs to make 500 L of a 34% acid solution for a customer. The lab has 25% and 50% acid solutions available to make the order. How many litres of each should be mixed to make the 34% solution?</p>
<p>How many quarts of pure orange juice should Michael add to a 10% orange drink to create 6 quarts of a 40% orange juice mixture? Let <code class='latex inline'>p</code> represent the number of quarts of pure orange juice he should add to the orange drink.</p><p>How much 10% juice should Michael use?</p>
<p>Eula Jones is investing \$6000 in two accounts, part at 4.5% and the remainder at 6%. If <code class='latex inline'>d</code> represents the number of dollars invested at 4.5%, which expression represents the amount of interest earned in the account paying 6%?</p><p>A. <code class='latex inline'>0.06d</code></p><p>B. <code class='latex inline'>0.06(d-6000)</code></p><p>C. <code class='latex inline'>0.06(d+6000)</code></p><p>D. <code class='latex inline'>0.06(6000-d)</code></p>
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