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<p><strong> Students will compleste the following questions to practice the skills they have learned in this lesson.<br>
</strong></p>
<ol class="os-raise-noindent" start="1">
<li> Translate to an equation: Which equation means nine more than \(x\) is equal to 52?<br>
</ol>
</li>
<ul>
<li> \(x+9=52\) </li>
<li>\(9x=52\)</li>
<li>\(9-x=52\)</li>
<li>\(\frac{\;52}x=9\)</li>
</ul>
<p><strong>Answer:</strong> \(x + 9 = 52\)</p>
<p>Nine more than \(x\) means that 9 is added to \(x\).<br>
\(x+9\)<br>
Equal to 52 means that we take whatever expression that is in front of 52 and set them equal to each other.<br>
\(x+9=52\)</p>
<ol class="os-raise-noindent" start="2">
<li> Translate to an equation: Which equation means ten less than \(m\) is −14?
</ol>
</li>
<ul>
<li> \(10-m=-14\) </li>
<li> \(m-10=14\) </li>
<li> \(m-10=-14\) </li>
<li> \(-14-m=10\) </li>
</ul>
<p><strong>Answer:</strong> \( m - 10 = -14\)</p>
<p>Ten less than \(m\) means that 10 is subtracted from \(m\).<br>
\(m-10\)<br>
The word is, is the same as “equal to”. This means we take whatever expression that is in front of -14 and set them equal to each other.<br>
\(m-10=-14\)</p>
<ol class="os-raise-noindent" start="3">
<li> Translate to an equation: Which equation means the sum of \(y\) and −30 is 40?
</ol>
</li>
<ul>
<li> \(-30y=40\) </li>
<li> \(y= 40+-30\) </li>
<li> \(y+40=-30\) </li>
<li> \(y+(-30)=40\) </li>
</ul>
<p><strong>Answer:</strong> \( y + (-30) = 40\)</p>
<p>The sum of \(y\) and -30 means that you add them together.<br>
\(y+(-30)\)<br>
The word is, is the same as “equal to”. This means we take whatever expression that is in front of 40 and set them equal to each other.<r></r>
\(y+(-30)=40\)</p>
<ol class="os-raise-noindent" start="4">
<li> Translate to an equation: For a family birthday dinner, Celeste bought a turkey that weighed 5 pounds less than
the one she bought for Thanksgiving. The birthday turkey weighed 16 pounds. How much did the Thanksgiving turkey
weigh? <br>
</ol>
</li>
<ul>
<li> \(5-x=16\) </li>
<li> \(x-5=16\) </li>
<li> \(x+5=16\) </li>
<li> \(-x+5=16\) </li>
</ul>
<p><strong>Answer:</strong> \(x - 5 = 16\)</p>
<p>The important facts from the problem are that the weight of the birthday turkey is 16 pounds and that it is 5 pounds less than the Thanksgiving turkey.<br>
Choose a variable, \(x\), to represent the Thanksgiving turkey. <br>
The birthday turkey was 5 pounds less than the one she bought for Thanksgiving.<br>
\(x-5\)<br>
We also know the birthday turkey is 16 pounds. So they can be set equal to each other.<br>
\(x-5=16\)</p>
<ol class="os-raise-noindent" start="5">
<li> Translate to an equation: Which equation represents 45% of 120?
</ol>
</li>
<ul>
<li> \(x=45(120)\) </li>
<li> \(x=4.5(120)\) </li>
<li> \(x=0.45(120)\) </li>
<li> \(x=45+120\) </li>
</ul>
<p><strong>Answer:</strong> \(x = 0.45(120)\)</p>
<p>45% is equivalent to \(\frac{45}{100}\) or 0.45.<br>
The word “of” means that you need to multiply the two numbers together. <br>
.45 times 120 or \(0.45(120)\)
</p>
<ol class="os-raise-noindent" start="6">
<li> Translate to an equation: 250% of 65 can also be written as: <br>
</ol>
</li>
<ul>
<li> 2.5(65) </li>
<li> 0.25(65) </li>
<li> 25 (65) </li>
<li> 250(65) </li>
</ul>
<p><strong>Answer:</strong> 2.5(65) </p>
<p>250% is equivalent to <br>
\(\frac{250}{100}\) or 2.5<br>
The word “of” means that you need to multiply the two numbers together. <br>
2.5 times 65 or \(2.5(65)\)
</p>
<ol class="os-raise-noindent" start="7">
<li> Translate to an equation: Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25.
Geneva wants to leave 16% of the total bill as a tip. How much should the tip be?
</ol>
</li>
<ul>
<li> \(t=16(74.25)\) </li>
<li> \(t = 0.16(74.25)\) </li>
<li> \(t = 1.6(74.25)\) </li>
<li> \(t =16+(74.25)\) </li>
</ul>
<p><strong>Answer:</strong> \(t = 0.16(74.25)\)</p>
<p>The tip is a percentage of the bill so 16% of 74.25.<br>
16% is equivalent to <br>
\(\frac{16}{100}\) or 0.16<br>
The word “of” means that you need to multiply the two numbers together. <br>
0.16 times 74.25 or \(0.16(74.25)\)
</p>
<ol class="os-raise-noindent" start="8">
<li> Large cheese pizzas cost $5 each, and large one-topping pizzas cost $6 each.<br>
Choose the equation that represents the total cost, \(T\), of \(c\) large cheese pizzas and \(d\) large one-topping
pizzas.
</ol>
</li>
<ul>
<li>\(T=6c+5d\)</li>
<li>\(T=5c+6d\)</li>
<li>\(T=5c-6d\)</li>
<li>\(T=6c-5d\)</li>
</ul>
<p><strong>Answer:</strong> \( T=5c+6d \)<br> </p>
<p>Our equation in words would be that total cost is going to equal (the cost of one cheese pizza times the number of cheese pizzas purchased) plus (the cost of one one-topping pizza times the number of one-topping pizzas purchased).
</p>
<p>Substitute in the variables and prices that are given in the problem.<br>
\(T=5c+6d\)</p>
<ol class="os-raise-noindent" start="9">
<li> Jada plans to serve milk and healthy cookies for a book club meeting. She is preparing 12 ounces of milk and 4
cookies per person. Including herself, there are 15 people in the club. A package of cookies contains 24 cookies and
costs $4.50. A 1-gallon jug of milk contains 128 ounces and costs $3. Let \( n \) represent the number of people in
the club, \(m\) represent the ounces of milk, \(c\) represent the number of cookies, and \(b\) represent
Jada’s budget in dollars.
</ol>
</li>
<p><strong>Select two</strong> of the equations that could represent the quantities and constraints in this situation.
</p>
<ul>
<li>\(m=12(15) \)</li>
<li> \(3m+4.5c=b\)</li>
<li> \(4n=c\)</li>
<li> \(4(4.50)=c\)</li>
<li> \(b=2(3)+3(4.50)\)</li>
</ul>
<p class="os-raise-text-bold">Answer:</p>
<p>The correct answers are: \(m=12(15)\), \(4n=c\), and \(b=2(3)+3(4.50)\). </p>
<p>The three equations that could represent the quantities and constraints in this situation are:</p>
<p>\(m=12(15)\), represents the amount of milk that needs to be purchased is the amount each person will receive multiplied by the number of people in the club. This solution only works if there are 15 people in the club.</p>
<p>\(4n=c\), represents the number of cookies that each person will receive times the variable \(n\) which represents the number of people in the club equals the number of cookies that need to be purchased. This solution can work for any amount of club members.</p>
<p>\(b=2(3)+3(4.50)\), represents Jada’s budget. The number of 1-gallon jugs of milk she needs times the cost of each jug, 2(3). Plus the number of packages of cookies she needs times the cost of each package, 3(4.50). She needs 12(15)=180 ounces of milk. She will purchase \(\frac{180}{128}=1.41\) gallon jugs, but since she can’t buy .41 of a jug, she will have to buy 2 of them at $3.00 each. . She needs 4(15)=60 cookies. She has to purchase \(\frac{60}{24}=2.5\) packages, but since she can‚t buy .5 of a package, she will have to buy 3 of them at $4.50 each. This solution can only work if she does not need more that 180 ounces of milk or 60 cookies and if the jugs of milk cost exactly $3.00 and the packages of cookies cost exactly $4.50. </p>