Now You Try

<p>Claire has $50 in her piggy bank. She takes $2.50 from it each week to buy a hot chocolate a banana from the cafeteria. Create a table of values, a graph, and an equation to describe the amount of money in the piggy bank each week. </p>

<p>Leah earns <code class='latex inline'>\$1200</code>/month plus <code class='latex inline'>3.5\%</code> commission.</p><p><strong>(a)</strong> Create an equation that she can use to check her paycheque.</p><p><strong>(b)</strong> Last month, Leah had <code class='latex inline'>\$96 174</code> in sales. Her pay before deductions was <code class='latex inline'>\$4566.09</code>. Is this amount correct? Explain your answer.</p>

<p>This graph shows the maximum heart rate a person should try to achieve while exercising.</p><p>a) What does the y-intercept mean?</p><p>b) What does the slope represent?</p><p>c) Write an equation for the line.</p><p>d) Estimate the maximum heart rate for a 58-year-old.</p><img src="/qimages/25276" />

<p>Hank sells furniture and earns <code class='latex inline'>\$280</code>/week plus <code class='latex inline'>4\%</code> commission. </p><p><strong>(a)</strong> Determine the sales that Hank needs to make to meet his weekly budge requirement of <code class='latex inline'>\$900</code>.</p><p><strong>(b)</strong> Write an equation for this situation.</p>

<p>A promoter is holding a video dance. Tickets cost <code class='latex inline'>\$15</code> per person, and he has given away 10 free tickets to radio stations. </p>
<ul>
<li>Create the linear relation that models the money the promoter will earn in ticket sales in terms of the number of people attending the dance.</li>
</ul>

<p>Adriana earns <code class='latex inline'>5\%</code> commission on her sales up to <code class='latex inline'>\$25 000</code>, <code class='latex inline'>5.5\%</code> on any sales between <code class='latex inline'>\$25 000</code> and <code class='latex inline'>\$35 000</code>, <code class='latex inline'>6\%</code> on any sales between <code class='latex inline'>\$35 000</code> and <code class='latex inline'>\$45 000</code>, and <code class='latex inline'>7\%</code> for any sales over <code class='latex inline'>\$45 000</code>. What sales volume does she need to earn <code class='latex inline'>\$2000</code>?</p>

<p>An equation for a house’s value is
<code class='latex inline'>y = 7500x + 125 000</code>, where <code class='latex inline'>y</code> is the
value in dollars and <code class='latex inline'>x</code> is the time in years, starting now.</p><p><strong>a)</strong> What is the current value of the house?</p><p><strong>b)</strong> What is the value of the house 2 years from now?</p><p><strong>c)</strong> Determine the value of the house in 7 years.</p><p><strong>d)</strong> At what rate is the house value changing from year to year?</p>

<p>The amount of money in Alexander’s account is <code class='latex inline'>y = 4000 -70x</code>, where <code class='latex inline'>y</code> is the amount in dollars and x is the time in weeks.</p><p><strong>a)</strong> Which variable is independent and which is dependent?</p><p><strong>b)</strong> How do you know the relation is linear?</p><p><strong>c)</strong> Determine the rate of change of the money in Alexander’s account.</p><p><strong>d)</strong> What does the rate of change mean?</p><p><strong>e)</strong> How does the rate of change relate to the equation? </p><p><strong>f)</strong> When will Alexander’s account be empty?</p>

<p>Courtney paid a one-time registration fee to join a fitness club. She also pays a monthly fee. After three months, she had paid <code class='latex inline'>\$315</code>. After seven months, she had paid <code class='latex inline'>\$535</code>. Determine the registration fee and the monthly fee.</p>

<p>The Perfect Paving Company charges <code class='latex inline'>\$10</code> per square foot to install interlocking paving stones, as well as a <code class='latex inline'>\$40</code> delivery fee.</p>
<ul>
<li>Andrew needs to include 5 cubic yards of sand, costing <code class='latex inline'>\$15</code> per cubic yard, to the total cost of the project. How much will this added cost reduce the area that he can pave with his <code class='latex inline'>\$3500</code> budget?</li>
</ul>

<p>Marie earns $1 for every 4 papers she delivers.</p><p><strong>a)</strong> Show that the relation between papers delivered and money earned is linear, using a graph and a table of values.</p><p><strong>b)</strong> What do the first differences mean?</p><p><strong>c)</strong> What is the rate of change of Marie’s earnings?</p><p><strong>d)</strong> Predict Marie’s earnings for delivering 275 papers using an equation.</p>

<p>Cam earns <code class='latex inline'>\$400</code>/week plus <code class='latex inline'>2.5\%</code> commission. He has been offered another job that pays <code class='latex inline'>\$700</code>/week but no commission.</p><p> Which job should Cam take? Justify your decision.</p>

<p>Jane's Restaurant charges <code class='latex inline'>\$22.95</code> for brunch but allows one person per table to eat free. To figure out how many people attended the Sunday brunch, Jack collected the information in this table.</p><img src="/qimages/2589" /><p><em>a)</em> Why is it reasonable that Jack used the equation <code class='latex inline'>22.95(x - 1) = T</code> to determine the number of people at each table? What do the variables <code class='latex inline'>x</code> and <code class='latex inline'>T</code> represent?</p><p><em>b)</em> Create and solve the equation for each table number.</p><p><em>c)</em> How many people in total sat at the five tables?</p>

<p>A student athletic council raised <code class='latex inline'>\$4000</code> for new sports equipment and uniforms, which will be purchased <code class='latex inline'>3</code> years from now. Until then,
the money will be invested in a simple interest savings account that pays <code class='latex inline'>3.5 \%/year</code>.</p><p><strong>(a)</strong> Write an equation to represent the relationship between time (in years) and the total value of their investment.</p><p><strong>(b)</strong> Use the equation to determine the value of their investment after 2 years.</p><p><strong>(c)</strong> Use the equation to determine when their investment is worth <code class='latex inline'>\$4385</code>.</p>

<p>Melanie drove at <code class='latex inline'>100km/h</code> from Ajax to Ottawa. She left Ajax at 2:15 pm with <code class='latex inline'>35 L</code> of gas in the tank. The low fuel warning light came on when <code class='latex inline'>9 L</code> was left in the tank. If Melanie's SUV uses fast at the rate of <code class='latex inline'>9.5 L/100km</code>, estimate when light came on.</p>

<p>The Perfect Paving Company charges <code class='latex inline'>\$10</code> per square foot to install interlocking paving stones, as well as a <code class='latex inline'>\$40</code> delivery fee.</p>
<ul>
<li>Determine the greatest area that Andrew can pave for <code class='latex inline'>\$3500</code>.</li>
</ul>

<p>A van's gas tank holds 75 L. The van uses 0.125L/km. </p><p><strong>a)</strong> Describe the relation between the distance the van travels and the volume of gas in its tank.</p><p><strong>b)</strong> How far can the van travel on a full tank of gas?</p>

<p>Maria has budgeted <code class='latex inline'>\$90</code> to take her grandmother for a drive. Katie's Cars rents cars for <code class='latex inline'>\$65</code> per day plus <code class='latex inline'>\$0.12/km</code>. Determine how far Maria and her grandmother can travel, including the return trip.</p>

<p>Mike pays a <code class='latex inline'>\$350</code> registration fee and an <code class='latex inline'>\$85</code> monthly fee to belong to a fitness club has a higher registration fee but a lower monthly fee. After five months, both Mike and Lia have paid <code class='latex inline'>\$775</code>. Determine the equation which describes possible fees at Lia's club.</p>

<p>Apple juice is leaking rom a carton at the rate of <code class='latex inline'>5</code> mL/min. There are <code class='latex inline'>1890</code> mL of juice in the container at 10:00 am. </p><p><strong>(a)</strong> Write and equation for this situation.</p><p><strong>(b)</strong> When will <code class='latex inline'>1 L</code> of juice be left in the carton?</p>