Now You Try

<p>Over the years, the height of the Great Pyramid at Giza, Egypt, has decreased.</p><img src="/qimages/24382" /><p>Write an addition equation to represent the situation.</p>

<p>Translate each phrase into an algebraic expression.</p>
<ul>
<li>Twice a number, subtracted from five, is three more than seven times the number.</li>
</ul>

<p>Jonah is planting a rectangular garden. The perimeter of the garden is 120 yd, and the width is 20 yd. What is the length of the garden?</p>

<p>Solve each problem by working backward.</p><p>In the Trivia Bowl, each finalist must answer four questions correctly.
Each question is worth twice as much as the question before it. The fourth question is worth $6000. How much is the first question worth?</p>

<p>Over the years, the height of the Great Pyramid at Giza, Egypt, has decreased.</p><p>What was the decrease in the height of the pyramid?</p>

<p> In an isosceles triangle, the equation <code class='latex inline'>a+ 2b = 180^o</code> relates the two equal angles and the third angle.</p><p>Use this equation to find the value of <code class='latex inline'>b</code> when</p><p>i. <code class='latex inline'>a = 40^o</code>
ii. <code class='latex inline'>a = 100^o</code> </p><img src="/qimages/1142" />

<p> In an isosceles triangle, the equation <code class='latex inline'>a + 2b = 180^o</code> relates the two equal angles and the third angle.</p><p>Use this equation to find the value of <code class='latex inline'>a</code> when</p><p>i. <code class='latex inline'>b = 25^o</code>
ii. <code class='latex inline'>a = 100^o</code></p><img src="/qimages/1142" />

<p>If <code class='latex inline'>l</code> represents the length of a person’s foot in inches, the expression <code class='latex inline'>2l-12</code> can be used to estimate his or her shoe size.</p><p>What is the approximate length of the foot of a person who wears size 8?</p>

<p>The sum of one-half of a number, <code class='latex inline'>q</code> and thee-fifths is two-thirds the number is <code class='latex inline'>q</code>, Determine the number.</p>

<p>Justine’s mother is building an ultralight airplane. The fuel tank is made of plastic and has a mass of 5000 g. Each litre of gasoline has a mass of 840 g. The total mass of the fuel plus the tank cannot exceed 21 800 g.</p><p>The equation that represents this situation is: <code class='latex inline'>5000+840n=218000</code>.</p><p> Solve the equation to determine the number of litres of fuel in a full tank.</p>

<p>Write a real-life problem that can be modeled by an equation equivalent to the equation <code class='latex inline'>\displaystyle 5 x=30 . </code> Then solve the equation and write the answer in the context of your real-life problem.</p>

<p>Traditionally, nails are given names such as 2-penny, 3-penny, and so on. These names describe the lengths of the nails. What is the name of a nail that is <code class='latex inline'>2\frac{1}{2}</code> inches long?</p><img src="/qimages/24492" />

<p>Write an equation for each problem. Then solve the equation and check your solution.</p><p>Determine whether <code class='latex inline'>x+0=x</code> is sometimes, always, or never true. Explain your reasoning.</p>

<p>Write an equation and solve each problem.</p><p>Twenty-nine is thirteen added to four times a number. What is the number?</p>

<p>A midsize car with a 4-cylinder engine goes 10 miles more on a gallon of gasoline than a luxury car with an 8-cylinder engine. A midsize car consumes one gallon of gas for every 34 miles driven.</p><p>A subcompact car with a 3-cylinder engine goes 13 miles more than a luxury car on one gallon of gas. How far does a subcompact car travel on a gallon of gasoline?</p>

<p>Which equation represents the phrase "six more than
twice a number is <code class='latex inline'> 72^{\prime \prime} ? </code> </p><p><code class='latex inline'>\displaystyle
6+x=72
</code></p><p><code class='latex inline'>\displaystyle
2+6 x=72
</code></p><p><code class='latex inline'>\displaystyle
2 x=6+72
</code></p><p><code class='latex inline'>\displaystyle
6+2 x=72
</code></p>

<p>A baker orders 162 eggs. Each carton contains 18 eggs. Which equation can you use to find the number <code class='latex inline'>\displaystyle x </code> of cartons? Explain your reasoning and solve the equation.</p><p><code class='latex inline'>\displaystyle \begin{array}{ll}\text { (A) } 162 x=18 & \text { (B) } \frac{x}{18}=162 \ \text { (C) } 18 x=162 & \text { (D) } x+18=162\end{array} </code></p>

<p>Write an equation and solve each problem.</p><p>Six less than two thirds of a number is negative ten. Find the number.</p>

<img src="/qimages/42635" /><p>THOUGHT PROVOKING Draw</p><p>a different figure that has</p><p>the same perimeter as the</p><p>triangle shown. Explain</p><p>why your figure has the</p><p>same perimeter.</p>

<p>Write an equation for each problem. Then solve the equation and check your solution.</p><p>Determine whether <code class='latex inline'>x+x=x</code> is sometimes, always, or never true. Explain your reasoning.</p>

<p>For questions 58–61, use the graph to write an equation for each situation. Then solve the equation.</p><img src="/qimages/24383" /><p>How many more volumes does the Library of Congress have than the Harvard University Library?</p>

<p>A midsize car with a 4-cylinder engine goes 10 miles more on a gallon of gasoline than a luxury car with an 8-cylinder engine. A midsize car consumes one gallon of gas for every 34 miles driven.</p><p>How many more miles does a subcompact travel on a gallon of gasoline than a midsize car?</p>

<p>Solve each problem by working backward.</p><p>A bacteria population triples in number each day. If there are 2,187,000 bacteria on the seventh day, how many bacteria were there on the first day?</p>

<p>Translate each phrase into an algebraic expression.</p>
<ul>
<li>One fifth of a number, decreased by 17, is 41.</li>
</ul>

<p>Solve each problem by working backward.</p><p>A firefighter spraying water on a fire stood on the middle rung of a ladder. The smoke lessened, so she moved up 3 rungs. It got too hot, so she backed down 5 rungs. Later, she went up 7 rungs and stayed until the fire was out. Then, she climbed the remaining 4 rungs and went into the building. How many rungs does the ladder have?</p>

<p>Solve each problem by working backward.</p><p>A number is multiplied by seven, and then the product is added to 13. The result is 55. What is the number?</p>

<p>If <code class='latex inline'>16+4x</code> is 10 more than 14, what is the value of <code class='latex inline'>8x</code>?</p><p>A) 2</p><p>B) 6</p><p>C) 16</p><p>D) 80</p>

<p>Adele Jones is on a business trip and plans to rent a subcompact car from Speedy Rent-A-Car. Her company has given her a budget of $60 per day for car rental. What is the maximum distance Ms. Jones can drive in one day and still stay within her budget?</p><img src="/qimages/24467" />

<p>Write an equation and solve each problem.</p><p>Find three consecutive odd integers whose sum is 51.</p>

<p>Write an equation to model each situation. Then solve the equation.</p><p>You have a part-time job. You work for 3 h on Friday and 6 h on Saturday. You also receive an allowance of $20 per week. You earn $92 per week. How much do you earn per hour at your part-time job?</p>

<p>Solve each problem by working backward.</p><p>Nine is subtracted from a number, and then the difference is multiplied by 5. The result is 75. What is the number?</p>

<p>What is the length of a rectangle with width 10 in. and area <code class='latex inline'>45 in^2</code>?</p>

<p>About 4.9 million households had one brand of personal computers in 2001. The use of these computers grew at an average rate of 0.275 million households a year. In 2001, about 2.5 million households used another type of computer. The use of these computers grew at an average rate of 0.7 million households a year. How long will it take for the two types of computers to be in the same number of households?</p>

<p>Translate each phrase into an algebraic expression.</p>
<ul>
<li>The sum of the length and width of a backyard pool is <code class='latex inline'>96 m</code>.</li>
</ul>

<p>A midsize car with a 4-cylinder engine goes 10 miles more on a gallon of gasoline than a luxury car with an 8-cylinder engine. A midsize car consumes one gallon of gas for every 34 miles driven.</p><p>How many miles does a luxury car travel on a gallon of gasoline?</p>

<p>The interior angles of a polygon are the angles formed inside a polygon by two adjacent sides. The sum <code class='latex inline'>S</code> of the measures of the interior angles of a polygon with <code class='latex inline'>n</code> sides can be found using the formula <code class='latex inline'>S = 180(n - 2)</code>. The sum of a polygon's interior angle measures is <code class='latex inline'>1260^{\circ}</code>. How many sides does the polygon have?</p><p>a) What information are you given in the problem?</p><p>b) What variable do you need to solve for in the formula?</p>

<p>Solve each problem by working backward.</p><p>Hugo withdrew some money from his bank account. He spent one third of the money for gasoline. Then he spent half of what was left for a haircut. He bought lunch for $6.55. When he got home, he had $13.45 left. How much did he withdraw from the bank?</p>

<p>Translate each phrase into an algebraic expression.</p>
<ul>
<li>When tickets to a play cost <code class='latex inline'>\$5</code> each, the revenue at the box office is <code class='latex inline'>\$825</code>.</li>
</ul>

<p>A midsize car with a 4-cylinder engine goes 10 miles more on a gallon of gasoline than a luxury car with an 8-cylinder engine. A midsize car consumes one gallon of gas for every 34 miles driven.</p><p>Write an addition equation to represent the situation.</p>

<p>Solve each problem. Round to the nearest tenth, if necessary.</p><p>Bricklayers use the formula <code class='latex inline'>n = 7lh</code> to estimate the number <code class='latex inline'>n</code> of bricks needed to build a wall of length <code class='latex inline'>l</code> and height <code class='latex inline'>h</code>, where <code class='latex inline'>l</code> and <code class='latex inline'>h</code> are in feet. Solve the formula for <code class='latex inline'>h</code>. Estimate the height of a wall 28 ft long that requires 1568 bricks.</p>

<p>Polar stratospheric clouds are colorful clouds that form when temperatures fall below <code class='latex inline'>-78^{\circ}</code>. What is this temperature in degrees Fahrenheit?</p>