Now You Try

<p>Lina works at a greenhouse. She needs to plant a total of 32 bulbs. Two types of bulbs are available. She is asked to plant three times as many crocus bulbs as tulip bulbs. How many of each should she plant.</p>

<p>When you multiply a number, <code class='latex inline'>x</code>, by <code class='latex inline'>k</code>, add <code class='latex inline'>n</code>, and then divide by <code class='latex inline'>r</code>, the answer is <code class='latex inline'>w</code>.</p><p>The equivalent equation is </p><p><code class='latex inline'>
\displaystyle
\frac{xk + n}{r } = w
</code></p><p>Which of the following is rearrangement of equation above?</p><p>How is rearranging a relation or formula for a particular variable similar to isolating a variable in a linear equation? How is it different?</p>

<p>Jim looks in his TV cabinet and finds some old Beta and VHS tapes. He has 17 tapes in all. He finds that he has three more Beta grapes than VHS tapes. How many of each type does he have?</p>

<p> Dan drank 0.5 L of his bottle of milk then his brother John drank one third of a milk. There is 2 L of milk left over. How much milk was there in the beginning.</p>

<p>Amanda plans to make chocolate-chip cookies and oatmeal cookies for a bake sale. The chocolate-chip cookies use three eggs per batch. The oatmeal cookies use two eggs per batch. If Amanda makes 6 oatmeal cookies, how many chocolate-chip cookies did she make? Show your work.</p>

<p>The owner of a dart-throwing stand at a carnival pays <code class='latex inline'>75</code> cents every time the bull's-eye is hit, but charges <code class='latex inline'>25</code> cents every time it is missed.
After <code class='latex inline'>25</code> tries, Luke paid <code class='latex inline'>\$5.25</code>. How many times did he hit the bull's-eye?</p>

<p>Jacob has <code class='latex inline'>\$15</code> to buy muffins and doughnuts at the school bake sale, as a treat for the Camera Club. Muffins are <code class='latex inline'>75</code> cents each and doughnuts are <code class='latex inline'>25</code> cents each . How many muffins and doughnuts can he buy?</p><p><strong>(a)</strong> What is the maximum number of muffins that Jacob can buy?</p><p><strong>(b)</strong> What is the maximum number of doughnuts that he can buy?</p>

<p>A candy store is making a mixture of chocolate-coated almonds and <code class='latex inline'>n</code> chocolate—coated raisins. The almonds cost $30/kg and the raisins cost $8/kg. The total cost of the mixture is to be $150.</p><p>a. Write a linear relation expressing the total cost in terms of the mass of almonds and the mass of raisins purchased.</p><p>b. Write an equation to express the mass of almonds in terms of the mass of raisins.</p><p>c. Write an equation to express the mass of raisins in terms of the mass of almonds.</p><p>d. Which combinations of almonds and raisins will cost exactly $150?</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 <code class='latex inline'>840</code> g. The total mass of the fuel plus the tank cannot exceed <code class='latex inline'>21 800</code> g.</p><p> Write an equation that models the number of litres of gasoline that the tank may hold.</p>

<p>Aryn is planning to fly to Paris and then travel through Switzerland and Austria to Italy by train. On the day that she goes to buy the foreign currencies she needs, one euro costs <code class='latex inline'>\$1.40</code> and one Swiss franc cost <code class='latex inline'>\$0.90</code>. Which of the following can represent combinations of solution?</p>

<p>Gregory works half as many hours per week as Paul. Between the two, they work a total of 48 h one week.</p><p>a) Write an equation to represent the information in the first sentence.</p><p>b) Write an equation to represent the information in the second sentence.</p><p>c) Use the method of substitution to find the number of hours worked by each of them.</p>

<p>Define suitable variables for each situation, and write an equation:</p><p>Caroline has a day job and an evening job. She works a total of <code class='latex inline'>40</code> h/week.</p>

<p>Three quarter of a bottle is 10 L. How large is the bottle.</p>

<p>Deb pays <code class='latex inline'>10</code> cents/min for cell-phone calls and <code class='latex inline'>6</code> cents/text message. She has a budget of <code class='latex inline'>\$25/month</code> for both calls and text messages.</p><p>Which of the following is equivalent to the two linear relations described by above?</p>

<p>Chris is organizing a candy hunt for the children in her neighbourhood. He spent <code class='latex inline'>\$102</code> to buy 500 large candies and 400 small candies. The ratio of the price of a large candy to the price of a small candy is <code class='latex inline'>7:4</code>. Find the prices of one large and one small candy.</p>

<p>Find the number which when divided by 4 and increased by 12 is the same as when it is divided by 3 and decreased by 5.</p>

<p>At 9:00 a.m., Chantelle starts jogging north at <code class='latex inline'>6 km/h</code> from the south end of a <code class='latex inline'>21 km</code> trail. At the same time, Amit begins cycling south at <code class='latex inline'>15 km/h</code> from the north end of the same trail. Determine when they will meet.</p>

<p> If <code class='latex inline'>m</code> and <code class='latex inline'>n</code> are positive integers and <code class='latex inline'>m + n = 6</code>, which is a possible value for <code class='latex inline'>3m- 2n</code>?</p>
<ul>
<li><strong>A</strong> 4 </li>
<li><strong>B</strong> -4 </li>
<li><strong>C</strong> 0</li>
<li><strong>D</strong> 2</li>
<li><strong>E</strong> -2</li>
</ul>

<p>Define suitable variables for each situation, and write an equation. </p><p>Caroline earns <code class='latex inline'>\$15/h</code> at her day job and <code class='latex inline'>\$11/h</code> at her evening job. Last week, she earned <code class='latex inline'>\$540</code>.</p>

<p>When you multiply a number, <code class='latex inline'>x</code>, by <code class='latex inline'>k</code>, add <code class='latex inline'>n</code>, and then divide by <code class='latex inline'>r</code>, the answer is <code class='latex inline'>w</code>.</p>
<ul>
<li>Write the relation that models this situation.</li>
</ul>

<p>Ben's Bikes rents racing bikes for $25/day and mountain bikes for $30/day. Yesterday's rental charges were $3450.</p><p><strong>(a)</strong> Determine the greatest number of racing bikes that could have been rented.</p><p><strong>(b)</strong> Determine the greatest number of mountain bikes that could have been rented.</p><p><strong>(c)</strong> Write an equation to show the possible combinations of racing and mountain bikes rented yesterday.</p>

<p>The larger of two numbers is equal to 3 times the smaller number. The smaller number is equal to the larger number decreased by 30. Find the numbers.</p>

<p>When you multiply a number, <code class='latex inline'>x</code>, by <code class='latex inline'>k</code>, add <code class='latex inline'>n</code>, and then divide by <code class='latex inline'>r</code>, the answer is <code class='latex inline'>w</code>.</p><p>The equivalent equation is </p><p><code class='latex inline'>
\displaystyle
\frac{xk + n}{r } = w
</code></p><p>Solve the relation for <code class='latex inline'>x</code>.</p>

<img src="/qimages/43258" /><p>MATHEMATICAL CONNECTIONS Consider the</p><p>triangle shown.</p><p>a. Write a function that represents the perimeter of the triangle.</p><p>b. Identify the independent and dependent variables.</p><p>c. Describe the domain and range of the function. (Hint: The sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.)</p>

<p>Movie tickets are <code class='latex inline'>\$8</code> each and concert tickets are <code class='latex inline'>\$12</code> each. Andrew spent a total of <code class='latex inline'>\$100</code> on movie and concert tickets. </p><p>a. Write an equation to represent the total cost for movie and concert tickets. </p><p>b. Rewrite the equation in the form <code class='latex inline'>y =mx + b</code></p><p>c. Determine which of the following is a possible combinations of movie and concert tickets that Andrew might have bought.</p>

<p>A room contains three-legged stools and four-legged chairs. There are 48 legs altogether.</p><p>a) Write an equation to represent the relationship between the number of stools, the number of chairs, and the total number of legs.</p><p>b) How many stools could there be?</p>

<p>George is three times as old as Sam. Five years from now, the sum of their ages will be 46.</p><p><strong>(a)</strong> Create an equation that represents the relationship between George's and Sam's ages five years from now.</p><p><strong>(b)</strong> Use your equation to determine they current ages.</p>