(16) The ratio of John’s age to Lisa’s age is 3:2. If Lisa is 10 years old, how old is John?
- (a) 12 years
- (b) 15 years
- (c) 18 years
- (d) 20 years
Correct Answer: (b) 15 years
Let John’s age be \(3x\) years and Lisa’s age be \(2x\) years.
According to the problem, we have:
\[\frac{3x}{2x} = \frac{15}{10}\]
Cross-multiplying gives us:
\[3x \cdot 10 = 15 \cdot 2x\]
\[30x = 30x\]</latex><br />
The age of John is \(3x\) years.<br />
Therefore, John is 15 years old.</p>
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<p class="question"><b>(17)</b> In a group of friends, the ratio of males to females is 5:3. If there are 15 females in the group, how many males are there?</p>
<ul>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(a) 9 males</li>
<li class="option" data-correct="true" onclick="checkAnswer(this)">(b) 25 males</li>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(c) 20 males</li>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(d) 10 males</li>
</ul>
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<b>Correct Answer: (b) 25 males</b><br />
Let the number of males in the group be \(5x\) and the number of females be \(3x\).<br />
According to the problem, we have:<br />
[latex]\[\frac{5}{3} = \frac{5x}{15}\]
Cross-multiplying gives us:
\[5x = 15 \cdot \frac{5}{3}\]
\[5x = 25\]
\[x = 5\]</latex><br />
So, the number of males in the group is \(5x = 5 \cdot 5 = 25\).<br />
Therefore, there are 25 males in the group.</p>
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<p class="question"><b>(18)</b> The ratio of the prices of two laptops is 7:4. If the price of the cheaper laptop is $400, what is the price of the more expensive laptop?</p>
<ul>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(a) $225</li>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(b) $175</li>
<li class="option" data-correct="true" onclick="checkAnswer(this)">(c) $700</li>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(d) $1000</li>
</ul>
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<b>Correct Answer: (c) $700</b><br />
Let the price of the more expensive laptop be \(7x\) dollars and the price of the cheaper laptop be $400.<br />
According to the problem, we have:<br />
[latex]\[\frac{7x}{400} = \frac{7}{4}\]
Cross-multiplying gives us:
\[7x = 400 \cdot \frac{7}{4}\]
\[7x = 700\]
\[x = 100\]</latex><br />
So, the price of the more expensive laptop is \(7x = 7 \cdot 100 = $700\).<br />
Therefore, the price of the more expensive laptop is $700.</p>
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<p class="question"><b>(19)</b> The ratio of the ages of three siblings is 2:3:4. If the sum of their ages is 54 years, how old is the youngest sibling?</p>
<ul>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(a) 10 years</li>
<li class="option" data-correct="true" onclick="checkAnswer(this)">(b) 12 years</li>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(c) 14 years</li>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(d) 16 years</li>
</ul>
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<b>Correct Answer: (b) 12 years</b><br />
Let the ages of the siblings be \(2x\) years, \(3x\) years, and \(4x\) years, respectively.<br />
According to the problem, we have:<br />
[latex]\[2x + 3x + 4x = 54\]
\[9x = 54\]</latex><br />
[latex]\[x = 6\]</latex><br />
So, the age of the youngest sibling (\(2x\)) is \(2 \cdot 6 = 12\) years.<br />
Therefore, the youngest sibling is 12 years old.</p>
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<p class="question"><b>(20)</b> The ratio of the number of books on mathematics to the number of books on science in a library is 5:8. If there are 40 books on science, how many books are there on mathematics?</p>
<ul>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(a) 24 books on mathematics</li>
<li class="option" data-correct="true" onclick="checkAnswer(this)">(b) 25 books on mathematics</li>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(c) 32 books on mathematics</li>
<li class="option" data-correct="false" onclick="checkAnswer(this)">(d) 35 books on mathematics</li>
</ul>
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<b>Correct Answer: (b) 25 books on mathematics</b><br />
Let the number of books on mathematics be \(5x\) and the number of books on science be \(8x\).<br />
According to the problem, we have:<br />
[latex]\[\frac{5x}{8x} = \frac{5}{8}\]
Cross-multiplying gives us:
\[5x \cdot 8 = 8x \cdot 5\]
\[40x = 40x\]
The number of books on mathematics is \(5x\) books.
Therefore, there are 25 books on mathematics.
