Now You Try

<p>Alysia is designing a logo for her school team, the Eagles. The design will be used to make different-sized crests for clothing such as jackets, sweaters, and baseball caps. How can Alysia make sure that, when the crest is made larger or smaller, the shape will not change?
The height will always be double the width.</p><p>a) If w represents the width, what expression represents the height?</p><p>b) How high will a crest that is 5 cm wide be?</p><p>c) How wide will a crest that is 25 cm high be?</p>

<p>Write a ratio to compare each quantity to its total. Express each ratio in simplest form.</p><p><code class='latex inline'>\displaystyle 12 \mathrm{~g} </code> of fat in <code class='latex inline'>\displaystyle 96 \mathrm{~g} </code> of meat</p>

<p>Solve. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle 8: 6: 10=12: p: q </code></p>

<p>Solve. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle x: 9=5: 3 </code></p>

<p>A 3.6 m ladder is leaning against a wall, with its base 2 m from the wall.</p>
<ul>
<li>Suppose that a 2.4 m ladder is placed against the wall, parallel
to the longer ladder. Explain why the triangles that are formed
by the ground, the wall, and the two ladders are similar.</li>
</ul>

<p>A square photo, with an area of <code class='latex inline'>324.00 cm^2</code>, is in a square frame that has an area of <code class='latex inline'>142.56 cm^2</code>. The dimensions of the photo and
the frame are proportional.</p><p><strong>a)</strong> Determine the scale factor that relates the dimensions of the photo and the frame.</p><p><strong>b)</strong> Determine the width of the frame.</p>

<p>A collector’s model racecar is scaled so that 1 inch on the model equals <code class='latex inline'>6\frac{1}{4}</code> feet on the actual car. If the model is <code class='latex inline'>\frac{2}{3}</code> inch high, how high is the actual car?</p>

<p>Use cross products to determine whether each pair of ratios form a proportion. Write yes or no.</p><p><code class='latex inline'>\frac{4}{11}, \frac{12}{33}</code></p>

<p>Do any two of the ratios you wrote for Exercise 17 form a proportion? If so, explain the real-world meaning of the proportion.</p>

<p>A grocer has <code class='latex inline'>c</code> pounds of coffee divided equally among <code class='latex inline'>k</code> sacks. She finds <code class='latex inline'>n</code> empty sacks and decides to redistribute the coffee equally among the <code class='latex inline'>k + n</code> sacks. When this is done, how many fewer pounds of coffee does each of the original sacks hold?</p>

<p>The Lehmans’ minivan requires 5 gallons of gasoline to travel 120 miles. How much gasoline will they need for a 350-mile trip?</p>

<p>Write a ratio to compare each quantity to its total. Express each ratio in simplest form.</p><p><code class='latex inline'>\displaystyle 12 \mathrm{~L} </code> of water in <code class='latex inline'>\displaystyle 14 \mathrm{~L} </code> of juice</p>

<p> A bicycle gear ratio compares the number of teeth on the driver cog to the number of teeth on the driving cog. The driver cog on a bicycle has 30 teeth and the driving cog has 20 teeth.</p><img src="/qimages/1656" /><p>a) If the driver cog rotates three turns, how many turns does the driving cog make?</p><p>b) If the driver cog makes a half turn, how many turns does the driving cog make?</p><p>c) How many turns of the driver cog are required for the driving cog to turn five times?</p><p>d) On a different bicycle, the driver cog has 24 teeth and the driving cog has 40 teeth. If the driver cog makes a half turn, how many turns does the driving cog make?</p>

<p>a) <code class='latex inline'>\displaystyle \Lambda </code> rectangular yard measures <code class='latex inline'>\displaystyle 8 \mathrm{~m} </code> by <code class='latex inline'>\displaystyle 6 \mathrm{~m} </code>. What happens to the area if each</p><p>dimension is doubled?</p><p>b) Use an appropriate tool to illustrate what happens to the area of any rectangle</p><p>when its dimensions are doubled.</p>

<p>Seth earns $152 in 4 days. At that rate, how many days will it take him to earn $532?</p>

<p>Describe how to solve a proportion if one of the ratios contains a variable.</p>

<p>Min is standing in a parking lot on a sunny day. He is <code class='latex inline'>1.8 m</code> tall and casts a shadow that is <code class='latex inline'>5.4 m</code> long.</p><p> Determine the length of the shadow cast by a nearby tree
that is 12.2 m tall.</p>

<p>A research study shows that three out of every twenty pet owners got their pet from a breeder. Of the 122 animals cared for by a veterinarian, how many would you expect to have been bought from a breeder?</p>

<p>John's school is 10 km away from his home. On his way to school, there is a 7/11 convenience store exactly 4 km from John's home. John is heading home. Currently he is 2 km from School. 1 hour later, John is 3 km to 7/11. How many km did he walk? </p>

<p>Lanette drove 248 miles in 4 hours. At that rate, how long will it take her to drive an additional 93 miles?</p>

<img src="/qimages/38509" /><p>SHORT RESPONSE Suppose each dimen sion rectangle <code class='latex inline'>\displaystyle A B C D </code> is doubled. What is the perimeter of the new <code class='latex inline'>\displaystyle A B C D ? </code></p>

<p>Use cross products to determine whether each pair of ratios form a proportion. Write yes or no.</p><p><code class='latex inline'>\frac{8}{9}, \frac{12}{18}</code></p>

<p>Write a ratio to compare each quantity to its total. Express each ratio in simplest form.</p><p><code class='latex inline'>\displaystyle 40 \mathrm{~mL} </code> of chlorine in <code class='latex inline'>\displaystyle 850 \mathrm{~mL} </code> of solution</p>

<img src="/qimages/1133" /><p>The density of this type of bass is about 10\% greater than that of water. which is <code class='latex inline'>1 g/cm^3</code>. Use the mass relationship <code class='latex inline'>density = \frac{mass}{volume}</code>
to estimate volume the mass of this bass after 3 months. To estimate the volume of the bass, find the volume of a rectangular prism with the same width, length, and height as the bass. </p>

<p> A circular garden has a diameter of 12 m. By how much should the diameter be increased to triple the area of the garden?</p>

<p>How wide is this bay?</p><img src="/qimages/1014" />

<p>Every ratio can be described as a fraction. Why can you describe the ratio of the can sizes as any of the following?</p><p><code class='latex inline'>3:2</code></p><p><code class='latex inline'>1:\frac{2}{3}</code></p><p><code class='latex inline'>\frac{3}{2}:1</code></p>

<p>Solve. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle 4: 1=p: 3 </code></p>

<p>To convert from centimetres to inches, you can use the fact that a 30 -cm ruler is just over 12 inches long. A person is <code class='latex inline'>\displaystyle 160 \mathrm{~cm} </code> tall. What is the person's approximate height, in inches?</p>

<p>Use cross products to determine whether each pair of ratios form a proportion. Write yes or no.</p><p><code class='latex inline'>\frac{2.3}{3.4}, \frac{3.0}{3.6}</code></p>

<p>A naturalist's study in Northern Ontario finds that 25% of the area is water and 60% of the remaining area is forest. The rest, 12 000 ha, is rock. How large is the study area, in hectares?</p><p><strong>A</strong> 36 000 ha</p><p><strong>B</strong> 40 000 ha</p><p><strong>C</strong> 68 000 ha</p><p><strong>D</strong> 80 000 ha</p><p><strong>E</strong> 100 000 ha</p>

<p>Solve. The first part has been done for you.</p><p><code class='latex inline'>\displaystyle 1.5: s=9: 15 </code></p>

<p>A 3.6 m ladder is leaning against a wall, with its base 2 m from the wall.</p>
<ul>
<li>Draw a scale diagram to represent this situation.</li>
</ul>

<p>Seven out of ten people prefer Fresh</p><p>toothpaste. How many would prefer Fresh</p><p>in a group of 120 people?</p>

<p>Write a ratio to compare each quantity to its total. Express each ratio in simplest form.</p><p><code class='latex inline'>\displaystyle 5 \mathrm{~kg} </code> of potassium in <code class='latex inline'>\displaystyle 20 \mathrm{~kg} </code> of fertilizer</p>