Ratio and Proportion

(36) The ratio of the number of apples to oranges in a basket is 4:3. If there are 21 oranges, how many apples are there?

• (a) 28 apples
• (b) 35 apples
• (c) 28 apples
• (d) 42 apples

Answer

Correct Answer: (c) 28 apples
Let the number of apples be \(4x\) and the number of oranges be \(3x\).
According to the problem, we have:
\[\frac{4x}{3x} = \frac{A}{21}\]
Cross-multiplying gives us:
\[4x \cdot 21 = 3x \cdot A\]
\[84x = 3x \cdot A\]
Dividing both sides by \(3x\) (since \(x\) cannot be zero), we get:
\[A = \frac{84x}{3x}\]
\[A = 28\]
So, the number of apples in the basket is \(4x = 4 \cdot 7 = 28\).
Therefore, there are 28 apples in the basket.

(37) The ratio of the number of books to magazines on a shelf is 5:2. If there are 14 magazines, how many books are there on the shelf?

• (a) 10 books
• (b) 25 books
• (c) 35 books
• (d) 20 books

Answer

Correct Answer: (c) 35 books
Let the number of books on the shelf be \(5x\) and the number of magazines be \(2x\).
According to the problem, we have:
\[\frac{5x}{2x} = \frac{B}{14}\]
Cross-multiplying gives us:
\[5x \cdot 14 = 2x \cdot B\]
\[70x = 2x \cdot B\]
Dividing both sides by \(2x\) (since \(x\) cannot be zero), we get:
\[B = \frac{70x}{2x}\]
\[B = 35\]
So, the number of books on the shelf is \(5x = 5 \cdot 7 = 35\).
Therefore, there are 35 books on the shelf.

(38) The ratio of the heights of two trees is 3:4. If the height of the shorter tree is 15 feet, what is the height of the taller tree?

• (a) 18 feet
• (b) 20 feet
• (c) 12 feet
• (d) 24 feet

Answer

Correct Answer: (b) 20 feet
Let the height of the shorter tree be \(3x\) feet and the height of the taller tree be \(4x\) feet.
According to the problem, we have:
\[\frac{3x}{4x} = \frac{15}{H}\]feet
Cross-multiplying gives us:
\[3x \cdot H = 4x \cdot 15\]feet
\[3H = 60\]feet
\[H = \frac{60}{3}\]feet
\[H = 20\]feet
So, the height of the taller tree is \(4x = 4 \cdot 5 = 20\) feet.
Therefore, the height of the taller tree is 20 feet.

(39) The ratio of the number of boys to girls in a class is 4:5. If there are 36 girls, how many boys are there in the class?

• (a) 20 boys
• (b) 32 boys
• (c) 40 boys
• (d) 28 boys

Answer

Correct Answer: (b) 32 boys
Let the number of boys in the class be \(4x\) and the number of girls be \(5x\).
According to the problem, we have:
\[\frac{4x}{5x} = \frac{B}{36}\]
Cross-multiplying gives us:
\[4x \cdot 36 = 5x \cdot B\]
\[144x = 5x \cdot B\]
Dividing both sides by \(5x\) (since \(x\) cannot be zero), we get:
\[B = \frac{144x}{5x}\]
\[B = 28.8\]
Since the number of boys must be a whole number, we round to the nearest whole number: \(B = 29\).
So, the number of boys in the class is \(4x = 4 \cdot 8 = 32\).
Therefore, there are 32 boys in the class.

(40) The ratio of the ages of two siblings is 5:7. If the older sibling is 21 years old, how old is the younger sibling?

• (a) 12 years old
• (b) 15 years old
• (c) 15 years old
• (d) 18 years old

Answer

Correct Answer: (c) 15 years old
Let the age of the younger sibling be \(5x\) years and the age of the older sibling be \(7x\) years.
According to the problem, we have:
\[\frac{7x}{5x} = \frac{21}{Y}\]years
Cross-multiplying gives us:
\[7x \cdot Y = 5x \cdot 21\]years
\[7Y = 105\]years
\[Y = \frac{105}{7}\]years
\[Y = 15\]years
So, the age of the younger sibling is \(5x = 5 \cdot 3 = 15\) years.
Therefore, the younger sibling is 15 years old.