Ratio and Proportion

(6) The ratio of the prices of two mobile phones is 5:4. If the price of the first phone is $400, what is the price of the second phone?

• (a) $320
• (b) $500
• (c) $320
• (d) $450

Answer

Correct Answer: (c) $320
Let the price of the second phone be \(4x\) dollars.
According to the problem, we have:
\[\frac{5}{4} = \frac{400}{4x}\]
Cross-multiplying gives us:
\[5 \cdot 4x = 400 \cdot 1\]
\[20x = 400\]
\[x = 20\]
So, the price of the second phone (\(4x\)) is \(4 \cdot 20 = 80\) dollars.
Therefore, the price of the second phone is $80.

(7) In a recipe, the ratio of sugar to flour is 2:5. If you need 400 grams of sugar, how many grams of flour should you use?

• (a) 1000 grams
• (b) 160 grams
• (c) 800 grams
• (d) 250 grams

Answer

Correct Answer: (a) 1000 grams
Let \(x\) represent the number of grams of flour needed.
According to the problem, we have:
\[\frac{2}{5} = \frac{400}{x}\]
Cross-multiplying gives us:
\[2x = 400 \cdot 5\]
\[2x = 2000\]
\[x = 1000\]
So, you should use 1000 grams of flour.

(8) The length and width of a rectangle are in the ratio of 3:4. If the perimeter of the rectangle is 28 meters, what is its area?

• (a) 24 square meters
• (b) 48 square meters
• (c) 36 square meters
• (d) 56 square meters

Answer

Correct Answer: (b) 48 square meters
Let the length of the rectangle be \(3x\) meters and the width be \(4x\) meters.
According to the problem, we have:
\[2(3x + 4x) = 28\]
\[2(7x) = 28\]
\[14x = 28\]
\[x = 2\]
So, the length of the rectangle is \(3x = 3 \cdot 2 = 6\) meters, and the width is \(4x = 4 \cdot 2 = 8\) meters.
The area of the rectangle is \(6 \cdot 8 = 48\) square meters.

(9) The ratio of the number of boys to the number of girls in a class is 5:7. If there are 35 girls in the class, how many boys are there?

• (a) 25 boys
• (b) 30 boys
• (c) 25 boys
• (d) 20 boys

Answer

Correct Answer: (c) 25 boys
Let the number of boys be \(5x\) and the number of girls be \(7x\).
According to the problem, we have:
\[\frac{5}{7} = \frac{5x}{35}\]
Cross-multiplying gives us:
\[5x = 35 \cdot 5\]
\[5x = 175\]
\[x = 35\]
So, the number of boys is \(5x = 5 \cdot 35 = 175\).
Therefore, there are 175 boys in the class.

(10) The ratio of the ages of a father and his son is 7:1. If the sum of their ages is 64 years, how old is the father?

• (a) 49 years
• (b) 56 years
• (c) 42 years
• (d) 63 years

Answer

Correct Answer: (b) 56 years
Let the age of the son be \(x\) years.
According to the problem, we have:
\[\frac{7}{1} = \frac{7x}{x}\]
Cross-multiplying gives us:
\[7x = 7 \cdot x\]
\[7x = 7x\]
The age of the father is \(7x\) years.
Since the sum of their ages is 64 years, we have:
\[x + 7x = 64\]
\[8x = 64\]
\[x = 8\]
So, the age of the father is \(7x = 7 \cdot 8 = 56\) years.
Therefore, the father is 56 years old.