Now You Try

<p>When a welder works for <code class='latex inline'>3 h</code> and an apprentice works for <code class='latex inline'>5 h</code>, they earn a total of <code class='latex inline'>\$175</code>. When the welder works for <code class='latex inline'>7 h</code> and the apprentice works for <code class='latex inline'>8 h</code>, they earn a total of <code class='latex inline'>\$346</code>. Determine the hourly rate for each worker.</p>

<p>Fitness centre A has a monthly membership fee of <code class='latex inline'>\$90</code>. Members pay $5 to take an aerobics class. At Fitness centre B, there is no membership fee, but clients pay <code class='latex inline'>\$10</code> per class.</p><p>a) Write a linear relation for the yearly cost in terms of the number of aerobics classes.</p><p>b) Graph the equations on the same set of axes.</p><p>c) State the point of intersection.</p><p>d) What does the point of intersection mean in this case?</p><p>e) How would you advise someone who is trying to choose between the two fitness clubs?</p>

<p>When a welder works for <code class='latex inline'>3 h</code> and an apprentice works for <code class='latex inline'>5 h</code>, they earn a total of <code class='latex inline'>\$175</code>. When the welder works for <code class='latex inline'>7 h</code> and the apprentice works for <code class='latex inline'>8 h</code>, they earn a total of <code class='latex inline'>\$346</code>. Determine the hourly rate for each worker.</p>

<p>Marie charges <code class='latex inline'>\$3</code> for every 4 bottles of water purchased from her store. She pays her supplier <code class='latex inline'>\$0.25</code> per bottle, plus <code class='latex inline'>\$250</code> for shelving and water delivery. </p><p><strong>(a)</strong> Create a system of two linear equations to model this situation. </p><p><strong>(b)</strong> How many bottles of water does she need to sell to break even?</p>

<p>A restaurant that serves a buffet lunch has one price for adults and another price for children under 12. The lung group has two adults and three children and their bill is $48.95. The Harvey group has three adults and two children. Their bill is $52.05. What is the price of the buffet for an adult? for a child?</p>

<p>Theatre tickets The receipts from 550 people attending a play
were <code class='latex inline'> \$ 9184 </code> . The tickets cost <code class='latex inline'> \$ 20 </code> for adults and <code class='latex inline'> \$ 12 </code> for students. The
relationship between the number of adult tickets sold, <code class='latex inline'> a </code> , and the number of
student tickets sold, <code class='latex inline'> s </code> , can be modelled by the following system of equations.</p><p><code class='latex inline'>\displaystyle
\begin{array}{l}
a+s=550 \\
20 a+12 s=9184
\end{array}
</code></p><p>a) Communication Interpret each equation in words.</p><p>b) Solve the system of equations to find the numbers of adult tickets and
student tickets sold.</p>

<p>Evan and Sara shovel driveway in the winter time to earn some money. They charge $10 for a double driveway and $5 for a single driveway. This past winter, Min earned $255 and Steve earned $230.</p><p>a. Write equations for both Evan and Sarah to represent the relationship between the
amounts earned shovelling single and double driveways.</p><p>b. Isolate the variable used for single driveways in both equations.</p><p>c. If they both shovelled 10 double driveways, how many single driveways did each shovel?</p>

<p>When a welder works for <code class='latex inline'>3 h</code> and an apprentice works for <code class='latex inline'>5 h</code>, they earn a total of <code class='latex inline'>\$175</code>. When the welder works for <code class='latex inline'>7 h</code> and the apprentice works for <code class='latex inline'>8 h</code>, they earn a total of <code class='latex inline'>\$346</code>. Determine the hourly rate for each worker.</p>

<p>A catering company charges $550 for 20 guests and $775 for 35 guests. What is the cost per person?</p>

<p>Lou’s class is selling T-shirts for a fundraiser. The supplier charges <code class='latex inline'>\$750</code> for the initial design and set-up plus <code class='latex inline'>\$5</code> for each imprinted T-shirt. The students sell the T-shirts for <code class='latex inline'>\$15</code> each.</p><p><strong>a)</strong> How many T-shirts do the students need to sell to break even?</p><p><strong>b)</strong> How much profit will the students make if they sell <code class='latex inline'>150</code> T-shirts?</p>

<p>Dan has saved <code class='latex inline'>\$500</code>. He wants to open a chequing account at Dominion Trust or Maple Leaf Savings. Which financial institution charges less per month if Dan uses 12 cheques a month?</p><p><strong>Dominion Trust:</strong></p>
<ul>
<li>monthly fee: <code class='latex inline'>\$10</code></li>
<li>cheque fee: <code class='latex inline'>\$0.75/cheque</code></li>
</ul>
<p><strong>Maple Leaf Savings:</strong></p>
<ul>
<li>monthly fee: <code class='latex inline'>\$7</code></li>
<li>cheque fee: <code class='latex inline'>\$1.00/cheque</code></li>
</ul>
<p><a href="https://youtu.be/GWIvslv_1iY">HINT</a></p>

<p>Evan spend a total of $18 on gourmet jellybeans and chocolate-covered almonds. The jellybeans cost $12/kg. The almonds cost $21/kg.</p><p>(a) Write an equation to represent Evan's purchases.</p><p>(b) Isolate the variable for the quantity of jellybeans in your equation.</p><p>(c) If Evan bought 250 g of almonds, how many grams of jellybeans did he buy?</p><p>(d) If Evan bought 100g of almonds, how many grams of jellybeans did he buy?</p>

<p>Nicole has been offered a sales job at Best Tech and a sales job at Best Tech. Which offer should Nicole accept? Explain.</p>
<ul>
<li><p>Best Tech: <code class='latex inline'>\$500</code> per week plus <code class='latex inline'>5\%</code> commission</p></li>
<li><p>Best Buy: <code class='latex inline'>\$400</code> per week plus <code class='latex inline'>7.5\%</code> commission</p></li>
</ul>

<p>Brenda has a total of <code class='latex inline'>41</code> loonies and toonies in her piggy bank. Their total value is <code class='latex inline'>\$59</code>.</p><p>(a) Write one equation for the total number of coins and a second equation for the total value.</p><p>(b) Graph both lines.</p><p>(c) Determine the coordinates of the point of intersection of the lines.</p>

<p>Jeff and Stephen go to the mall. The two boys buy a total of 15 T-shirts. Stephen gets three less than twice as many T-shirts as Jeff.</p><p><strong>a)</strong> Write an equation to represent the information in the second sentence.</p><p><strong>b)</strong> Write an equation to represent the information in the third sentence.</p><p><strong>c)</strong> Solve the linear system by substitution to find the number of T-shirts each boy bought.</p><p><strong>d)</strong> If the T-shirts cost <code class='latex inline'>\$8.99</code> each, how much did each boy spend before taxes?</p>

<p>A class trip is being planned. For one option, each student will pay $630. this includes two meals a day and accommodation for the 9-day trip. The other option offers three meals a day and accommodation for the 9 days. This second option costs $720. What is the cost per meal? What is the cost per day for accommodation?</p>

<p>Christina makes two types of leather belts. For the first type she charges $80
for the material and $50/h for labour. For the second type she charges $100 for the
material and $40/h for labour. For what number of hours are the costs the same?</p>

<p>All <code class='latex inline'>120</code> seats in a hall were filled for a concert. The tickets cost <code class='latex inline'>\$10</code> for adults and <code class='latex inline'>\$6</code> for students. The total proceeds were <code class='latex inline'>\$980</code>. </p><p>How many adults attended the concert? </p><p>How many students?</p>

<p>The caterers for a Grade 10 semi-formal dinner and dance are preparing two different meals: chicken at <code class='latex inline'>\$12</code> or pasta at <code class='latex inline'>\$8</code>. The total cost of the dinners for <code class='latex inline'>240</code> students is <code class='latex inline'>\$2100</code>.</p><p><strong>a)</strong> How many chicken dinners did the students order? </p><p><strong>b)</strong> How many pasta dinners did they order? </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>A student athletic council raised $6500 in a volleyball marathon. The students put some of the money in a savings account and the rest in a government bond. The rates are shown at the left. After one year, the students earned $235. How much did they invest at each rate? </p>

<p>As the owner of a banquet hall, you are in charge of catering a reception. You are serving two dinners: a chicken dinner that costs $20 and a fish dinner that costs $18. Two hundred guests have ordered their dinners in advance, and the total bill is $3880. </p><p><strong>a)</strong> Create a system of linear equations for this situation. </p><p><strong>b)</strong> Simplify and then solve the equivalent system to determine the number of each type of dinner ordered. </p>

<p>Min works in a department store selling sports equipment. Baseball gloves cost <code class='latex inline'>\$29</code> each and bats cost <code class='latex inline'>\$14</code> each. One shift, he sells 28 items. His receipts total <code class='latex inline'>\$ 647</code>.</p><p><strong>(a)</strong> How many bats did Min sell?</p><p><strong>(b)</strong> How many gloves did Min sell?</p>

<p>Tom pays a one-time registration charge and regular monthly fees to belong to a fitness club. After four months, he had paid <code class='latex inline'>\$420</code>. After nine months, he had paid <code class='latex inline'>\$795</code>. Determine the registration charge and the monthly fee.</p>

<p>A contractor rented a sander for <code class='latex inline'>5</code> hour and a polisher for <code class='latex inline'>5</code> hour for <code class='latex inline'>\$50</code>. For another job, she rented the sander for <code class='latex inline'>4</code> h and the polisher for <code class='latex inline'>8</code> h. </p><p>The rental fees for that job totaled <code class='latex inline'>\$56</code>. </p><p>Find the hourly rate charged for each tool.</p>

<p>Define suitable variables for each situation, and write an equation. </p>
<ul>
<li><p>a) Justin earns <code class='latex inline'>\$500</code>/week plus <code class='latex inline'>6\%</code> commission selling cars.</p></li>
<li><p>b) Justin is offered a new job that would pay <code class='latex inline'>\$800/week</code> plus <code class='latex inline'>4\%</code> commission.</p></li>
</ul>

<p>Fran and Winston have a combined income of $80 000. One quarter of Winston’s income is the same as one-sixth of Fran’s income. How much does each person earn?</p>

<p>A student athletic council raised $6500 in a volleyball marathon. The students put some of the money in a savings account and the rest in a government bond. After one year, the students earned $235. How much did they invest at each rate? </p>
<ul>
<li>The savings account interest rate is 3%</li>
<li>The bond account interest rate is 4%</li>
</ul>

<p>Fitness Club GoodFit charges a <code class='latex inline'>\$150</code> initial fee to join the club and a <code class='latex inline'>\$20</code> monthly fee. Fitness ’R' Us charges an initial fee of <code class='latex inline'>\$100</code> and <code class='latex inline'>\$30/month</code>.</p><p>a. Write an equation to represent the cost of membership at GoodFit.</p><p>b. Write an equation to represent the cost of membership at Fitness ’R' Us.</p><p>c. Graph the two lines which represents the two companies charge a member over time.</p><p>d. Find the point of intersection between <code class='latex inline'>C = 150 + 20n, C = 100 + 30n</code></p><p>e. If you are planning to join for 1 year, which club should you join? Explain your answer.</p>

<p>Tools-R-Us rents snow blowers for a base fee of <code class='latex inline'>\$20</code> plus <code class='latex inline'>\$8/h</code>. Randy's Rentals rents snowblowers for a base fee of <code class='latex inline'>\$12</code> plus <code class='latex inline'> \$10/h</code>.</p><p>a) Create an equation that represents the cost of renting a snowblower from Tools-R-Us.</p><p>b) Create the corresponding equation for Randy?s Rentals.</p><p>c) Solve the system of equations graphically.</p><p>d) What does the point of intersection mean in this situation?</p>

<p>The Tragically Hip Held a concert to help raise funds for local charities in their hometown of Kingston. A total of 15 000 people attended. The tickets were $8.50 per student and $12.50 per adult. The concert took in a total of $162 5000. How many adults came to the concert?</p>

<p>Allan plans to create a new coffee blend using Brazilian beans that cost <code class='latex inline'>\$12/kg</code> and Ethiopian beans that cost <code class='latex inline'>\$17/kg</code>. He is going to make <code class='latex inline'>150 kg</code> of the blend and sell it for <code class='latex inline'>\$14/kg</code>. </p>

<p>Juan is a cashier at a variety store. He has a total of <code class='latex inline'>\$580</code> in bills. He has <code class='latex inline'>76</code> bills, consisting of <code class='latex inline'>\$5</code> bills and <code class='latex inline'>\$10</code> bills. How many of each type does he have?</p>

<p>Joanne's family decides to rent a hall for her retirement party. Pin Hall charges <code class='latex inline'>\$500</code> for the hall and <code class='latex inline'>\$15</code> per meal. Bloom Place charges <code class='latex inline'>\$350</code> for the hall and <code class='latex inline'>\$18</code> per meal.</p><p><strong>a)</strong> Write two equation to represent the information.</p><p><strong>b)</strong> How many guests came to the party?</p>

<p>The caterers for a Grade 10 semi-formal dinner and dance are preparing two different meals: chicken at <code class='latex inline'>\$12</code> or pasta at <code class='latex inline'>\$8</code>. The total cost of the dinners for <code class='latex inline'>240</code> students is <code class='latex inline'>\$2100</code>.</p><p><strong>a)</strong> How many chicken dinners did the students order? </p><p><strong>b)</strong> How many pasta dinners did they order? </p>

<p>Allison is planning her parents’ 30th wedding anniversary dinner party. Abby Hall charges a fixed cost of <code class='latex inline'>\$1500</code> plus <code class='latex inline'>\$25</code> per guest. Bererkly Hall charges <code class='latex inline'>\$1000</code> plus <code class='latex inline'>\$30</code> per guest.</p><p>a) Write an equation for the cost at Abby Hall.</p><p>b) Write an equation for the cost at Bererkly Hall.</p><p>c) Use a graphing calculator to find the number of guests for which the charge is the same at both locations.</p><p>d) In what situation should Allison choose Abby Hall? Explain.</p><p>e) In what situation should Allison choose Berkely Hall? Explain.</p>

<p>Candice and Dino operate computer repair services. For a service call, Candice charges $40 and Dino charges $50. In addition, they each charge an hourly rate. Candice charges $35/h, and Dino charges $30/h. One day, their charges for two service calls were the same. What did they charge and how long did each person work?</p>

<p>Lily works at the ballpark selling bottled water. She sells 37 bottles in one shift. The large bottles sell for <code class='latex inline'>\$5</code> each and the small bottles els for <code class='latex inline'>\$3</code> each. At the end of one game, she has taken in <code class='latex inline'>\$131</code>.</p><p><strong>(a)</strong> How many large bottles did Liz sell?</p><p><strong>(b)</strong> How many small bottles did she sell?</p>

<p>The Video Stream you can watch movies for <code class='latex inline'>\$ 3.00/month</code> each and has no membership fee. At Rent Stream you can view movies for <code class='latex inline'>\$2/month</code> but has a <code class='latex inline'>\$15</code> membership fee.</p><p>a) Write an equation for each situation. </p><p>b) Graph both equations on the same set of axes. Find the point of intersection.</p><p>c) What does the point of intersection mean in this case?</p><p>d) What advice would you give to someone who is deciding which video store to use?</p>

<p>Sue is starting a lawn-cutting business. Her start-up cost to buy two A lawn mowers and an edge trimmer is <code class='latex inline'>\$665</code>. She has figured out that she will use about <code class='latex inline'>\$1</code> in gas for each lawn. If she charges <code class='latex inline'>\$20</code> per lawn, what will her break-even point be?</p>

<p>A Grade 10 class is raising money for a school— building project in Uganda. To buy 35 desks and 3 chalkboards, the students need to raise $2082. To buy 40 desks and 2 chalkboards, they need to raise $2238. Determine the cost of a desk and the cost of a chalkboard.</p>

<p>Some students at MGL held a bake sale recently to raise money for a field trip. They charged $7 for fruit pies and $10 for meat pies. They sold a total of 52 pies and earned $424. How many of each type of pie did they sell?</p>

<p>Bill wants to earn extra money selling lemonade in front of his house. It costs <code class='latex inline'>\$1.20</code> to start his business and each glass of lemonade costs <code class='latex inline'>\$0.06</code> to make. He plans to sell the lemonade for <code class='latex inline'>\$0.10</code> a glass.</p><p><strong>(a)</strong> Write an equation that represents his cost. </p><p><strong>(b)</strong> Write an equation that represents his revenue. </p><p><strong>(c)</strong> Graph both equations on the same set of axes. </p><p><strong>(d)</strong> What does the point of intersection mean in this case?</p><p><strong>(e)</strong> Does Bill make a profit or lose money for:</p>
<ul>
<li><em>i)</em> 20 glasses sold?</li>
<li><em>ii)</em> 35 glasses sold?</li>
<li><em>iii)</em> 50 glasses sold?</li>
</ul>

<p>The caterers for a Grade 10 semi-formal dinner and dance are preparing two different meals: chicken at <code class='latex inline'>\$12</code> or pasta at <code class='latex inline'>\$8</code>. The total cost of the dinners for <code class='latex inline'>240</code> students is <code class='latex inline'>\$2100</code>.</p><p><strong>a)</strong> How many chicken dinners did the students order? </p><p><strong>b)</strong> How many pasta dinners did they order? </p>

<p>Sarah is planning to visit relatives in England and Spain. On the day that she wants to buy the currencies for her trip, one euro costs <code class='latex inline'>\$1.50</code> and one British pound costs <code class='latex inline'>\$2.00</code>. Which of the equations represent combinations of these currencies can Sheila buy for <code class='latex inline'>\$700</code>? </p>

<p>Billy stops in at a pizza shop to get lunch for his crew. He buys five cheese and three vegetarian pizzas and the order costs $27.50. The next week, he pays $23.00 for two cheese and six vegetarian pizzas. How much does on roast beef sandwich cost?</p>

<p>A student athletic council raised $6500 in a volleyball marathon. The students put some of the money in a savings account and the rest in a government bond. The rates are shown at the left. After one year, the students earned $235. How much did they invest at each rate? </p>

<p>For a school band trip, Marco decides to order T-shirts for all of the participants. It will cost <code class='latex inline'>\$4</code> per shirt for the medium size, and <code class='latex inline'>\$5</code> per shirt for the large size. Marco orders a total of <code class='latex inline'>70</code> T-shirts and spends <code class='latex inline'>\$320</code>. How many are medium shirts?</p>

<p>Maria rented the same car twice in one month. She paid $180 the first 3 days and she drove a total of 150 km. The next time, she also paid $180 and had the vehicle for only 2 days, but travelled 400 km.</p><p><strong>(a)</strong> What was the cost per day?</p><p><strong>(b)</strong> What was the cost per kilometre?</p>

<p>To join Taekwondo club, Dave must pay a monthly fee of <code class='latex inline'>\$25</code> and an initial fee of <code class='latex inline'>\$200</code>. If he chooses Kool Karate, he must pay an initial fee of only <code class='latex inline'>\$100</code> but <code class='latex inline'>\$35/month</code>.</p><p><strong>(a)</strong> After how many months is the cost the same at either karate club?</p><p><strong>(b)</strong> If David plans to try karate for 6 months, which club should he join?</p><p><strong>(c)</strong> If David decides to do karate for a year, which club should he join?</p>

<p>Ready Car charges <code class='latex inline'>\$59/day</code> plus <code class='latex inline'>\$0.14/km</code> to rent a car. Best Car charges <code class='latex inline'>\$69/day</code> plus <code class='latex inline'>\$0.11/km</code>. Set up an equation which you can use to compare these two rental rates. What advice would you give someone who wants to rent a car from one of these companies? </p>

<p>Ron makes two types of comforters. To make the first type he charges $35 for the material and $60/h for labour. For the second type he charges $105 for the material and $25/h for labour. For what number of hours are the costs the same?</p>

<p>A restaurant that serves a buffet lunch has one price for adults and another price for children under 12. The lung group has two adults and three children and their bill is $48.95. The Harvey group has three adults and two children. Their bill is $52.05. What is the price of the buffet for an adult? for a child?</p>

<p>A total of 27 coins, in nickels and dimes, are in a wallet. If the coins total $2.15, how many of each type of coin are there?</p>