Now You Try

<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>A health-food company packs almond butter in jars. Some jars hold 250 g. Other jars hold 500 g. On Tuesday, the company packed 186.5 kg of almond butter in 511 jars. How many jars of each size did they pack?</p>

<p>Tim rows <code class='latex inline'>10</code> km downstream in <code class='latex inline'>2h</code>. On the return trip, it takes him <code class='latex inline'>4 h</code> to travel <code class='latex inline'>8 km</code>. Determine his average rowing speed and the speed of the current.</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>On weekends, as part of his exercise routine, Carl goes for a run, partly El on paved trails and partly across rough terrain. He runs at 10 km/h on the trails, but his speed is reduced to 5 km/h on the rough terrain. One day, he ran 12 km in 1.5 h. How far did he run on the rough terrain? </p>

<p>The Clarke's son suggest that they rent a car that costs $250 for the week plus 22 c/km. Their daughter does not want to drive far, so she suggests a car that is only $96 for the week but 50 c/km.</p><p>Write an equation to represent the cost of the car suggested by the daughter.</p>

<p>The difference between two angles in a triangle is <code class='latex inline'>11^{\circ}</code>. The sum of
the same two angles is <code class='latex inline'>77^{\circ}</code>. Determine the measures of all three angles in the triangle.</p>

<p>The Clarke's son suggest that they rent a car that costs $250 for the week plus 22 c/km. Their daughter does not want to drive far, so she suggests a car that is only $ 96 for the week but 50 c/km.</p>
<ul>
<li>When will the two cars cost the same? Use the method of elimination to solve.</li>
</ul>

<p>A train leaves Toronto for Montreal at the same time as another train leaves Montreal for Toronto. The cities are 500 km apart. The trains pass each other 2 h later. The train from Montreal is travelling 50km/h faster than the one from Toronto. At what distance away from Toronto do the trains pass each other?</p><p><a href="https://youtu.be/5Farc3F0xvI">Hint</a></p>

<p>The Clarke's son suggest that they rent a car that costs $250 for the week plus 22 c/km. Their daughter does not want to drive far, so she suggests a car that is only $96 for the week but 50 c/km.</p><p>What an equation to represent the cost of the car suggested by the son.</p>

<p>Carl travelled the 1900 km from his home in Eastern Ontario to Winnipeg. He travelled by bus to Toronto at an average speed of 60 km/h and then flew to Winnipeg at an average speed of 700 km/h. His total travelling time was 7 h. How many kilometres did he travel by bus? How far did he travel by airplane?</p>

<p>Wayne wants to use a few pieces of silver to make a bracelet. Some of the jewellery is <code class='latex inline'>80\%</code> silver, and the rest is <code class='latex inline'>66\%</code> silver. Wayne needs <code class='latex inline'>30.00g</code> of <code class='latex inline'>70\%</code> silver for the bracelet. How much of each alloy should he use?</p>

<p>Pietro needs to rent a truck for 1 day. He calls two rental companies to compare costs. Joe's Garage charges <code class='latex inline'>\$80</code> for the day plus <code class='latex inline'>\$0.22km</code>. Ace Trucks charges <code class='latex inline'>\$100/day</code> and <code class='latex inline'>\$0.12/km</code>. Under what circumstances do the two companies charge the same amount? When would it be better for Pietro to rent from Joe's Garage?</p>

<p>Jim researched these nutrition facts:</p>
<ul>
<li><code class='latex inline'>1g</code> of soy milk has <code class='latex inline'>0.005g</code> of carbo hydrates and <code class='latex inline'>0.030g</code> of protein.</li>
<li><code class='latex inline'>1g</code> of vegetables has <code class='latex inline'>0.14 g</code> of carbohydrates and <code class='latex inline'>0.030 g</code> of protein.</li>
</ul>
<p>Jim wants his lunch to have <code class='latex inline'>50.000</code> g of carbohydrates and <code class='latex inline'>20.000</code> g of protein. How many grams of soy milk and vegetables does he need?</p>

<p>With a tailwind, a plane flew the <code class='latex inline'>3000</code> km from Calgary to Montreal in <code class='latex inline'>5 h</code>. The return flight, against the wind, took <code class='latex inline'>6h</code>. Find the wind speed and the speed of the plane.</p>

<p>In a charity walkathon, Lori and Nicholas walked <code class='latex inline'>72.7</code> km. Lori walked <code class='latex inline'>8.9</code> km farther than Nicholas. </p><p><strong>a)</strong> Create a linear system to model this situation. </p><p><strong>b)</strong> Solve the system to determine how far each person walked. </p>

<p>To raise money for a local shelter, some Grade students held a car wash and charged the prices at the bottom. They washed 53 vehicles and raised<code class='latex inline'>\$382</code>.</p>
<ul>
<li>Car wash: <code class='latex inline'>\$6</code></li>
<li>Van wash: <code class='latex inline'>\$8</code></li>
</ul>
<p>How many of each type of vehicle did the students wash?</p>

<p>Ian flew his airplane at best cruise speed for 2h, then at economy cruise speed for 3h, covering a total of 850 km. On the following day, he flew what best bruise speed for 3 h and at economy cruise speed for 2h, covering a total of 900 km. Find the best cruise speed and the economy cruise speed for Ian's airplane.</p>

<p>In a charity walkathon, Lori and Nicholas walked <code class='latex inline'>72.7</code> km. Lori walked <code class='latex inline'>8.9</code> km farther than Nicholas. </p><p><strong>a)</strong> Create a linear system to model this situation. </p><p><strong>b)</strong> Solve the system to determine how far each person walked. </p>

<p>The perimeter of a beach volleyball court is 54 m. The difference between its length and its width is 9 m. </p><p>a) Create a linear system to model this situation. </p><p>b) Solve the system to determine the dimensions of the court. </p>

<p>A fishing boat took 3h to travel 36km upstream, against the current, on the St. Lawrence River. The same trip downstream only took 2 h. What is the average speed of the fishing boat in still water? What was the speed of the river current?</p>

<p>In a charity walkathon, Lori and Nicholas walked <code class='latex inline'>72.7</code> km. Lori walked <code class='latex inline'>8.9</code> km farther than Nicholas. </p><p><strong>a)</strong> Create a linear system to model this situation. </p><p><strong>b)</strong> Solve the system to determine how far each person walked. </p>

<p>On weekends, as part of his exercise routine, Carl goes for a run, partly El on paved trails and partly across rough terrain. He runs at 10 km/h on the trails, but his speed is reduced to 5 km/h on the rough terrain. One day, he ran 12 km in 1.5 h. How far did he run on the rough terrain? </p>