Ratio and Proportion

(26) The ratio of the number of marbles that are red to the number of marbles that are blue is 2:5. If there are 35 blue marbles, how many red marbles are there?

• (a) 7 red marbles
• (b) 12 red marbles
• (c) 14 red marbles
• (d) 17 red marbles

Answer

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

(27) The ratio of the number of apples to oranges in a basket is 3:2. If there are 20 oranges, how many apples are there?

• (a) 15 apples
• (b) 10 apples
• (c) 30 apples
• (d) 25 apples

Answer

Correct Answer: (c) 30 apples
Let the number of apples be \(3x\) and the number of oranges be \(2x\).
According to the problem, we have:
\[\frac{3x}{2x} = \frac{A}{20}\]
Cross-multiplying gives us:
\[3x \cdot 20 = 2x \cdot A\]
\[60x = 2x \cdot A\]
Dividing both sides by \(2x\) (since \(x\) cannot be zero), we get:
\[A = \frac{60x}{2x}\]
\[A = 30\]
So, the number of apples is \(3x = 3 \cdot 10 = 30\).
Therefore, there are 30 apples in the basket.

(28) The ratio of the prices of three shirts is 4:5:6. If the price of the cheapest shirt is $20, what is the price of the most expensive shirt?

• (a) $30
• (b) $24
• (c) $25
• (d) $28

Answer

Correct Answer: (b) $24
Let the price of the cheapest shirt be \(4x\) dollars and the prices of the other shirts be \(5x\) dollars and \(6x\) dollars.
According to the problem, we have:
\[\frac{4x}{20} = \frac{4}{5} = \frac{P}{X}\]dollars
Cross-multiplying gives us:
\[4x \cdot X = 20 \cdot 4\]dollars
\[4X = 80\]dollars
\[X = 20\]dollars
So, the price of the most expensive shirt (\(6x\)) is \(6 \cdot 20 = $24\).
Therefore, the price of the most expensive shirt is $24.

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

• (a) 36 boys
• (b) 45 boys
• (c) 30 boys
• (d) 45 boys

Answer

Correct Answer: (d) 45 boys
Let the number of boys be \(5x\) and the number of girls be \(4x\).
According to the problem, we have:
\[\frac{5x}{4x} = \frac{B}{36}\]
Cross-multiplying gives us:
\[5x \cdot 36 = 4x \cdot B\]
\[180x = 4x \cdot B\]
Dividing both sides by \(4x\) (since \(x\) cannot be zero), we get:
\[B = \frac{180x}{4x}\]
\[B = 45\]
So, the number of boys in the classroom is \(5x = 5 \cdot 9 = 45\).
Therefore, there are 45 boys in the classroom.

(30) The ratio of the ages of two friends is 2:3. If the older friend is 27 years old, how old is the younger friend?

• (a) 15 years old
• (b) 18 years old
• (c) 18 years old
• (d) 20 years old

Answer

Correct Answer: (c) 18 years old
Let the age of the younger friend be \(2x\) years and the age of the older friend be \(3x\) years.
According to the problem, we have:
\[\frac{3x}{2x} = \frac{27}{Y}\]years
Cross-multiplying gives us:
\[3x \cdot Y = 2x \cdot 27\]years
\[3Y = 54\]years
\[Y = 18\]years
So, the age of the younger friend is \(2x = 2 \cdot 18 = 18\) years.
Therefore, the younger friend is 18 years old.