Ratio word problems | Worsheets library - Free Printable

Problem: Ratio Word Problems

We are tasked with solving a series of ratio-based word problems. Let's go through each problem step by step.

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#### Problem 1:
The ratio of tomatoes to red apples is 2:5. If there are 20 tomatoes, how many red apples are there?

Solution:
1. The given ratio is 2:5, which means for every 2 tomatoes, there are 5 red apples.
2. Let the number of red apples be \( x \).
3. According to the ratio:
\[
\frac{\text{Tomatoes}}{\text{Red Apples}} = \frac{2}{5}
\]
4. Substituting the given number of tomatoes (20):
\[
\frac{20}{x} = \frac{2}{5}
\]
5. Cross-multiply to solve for \( x \):
\[
20 \cdot 5 = 2 \cdot x \implies 100 = 2x \implies x = \frac{100}{2} = 50
\]

Answer: There are 50 red apples.

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#### Problem 2:
The ratio of berries to oranges is 10:1. If there are 25 oranges, how many berries are there?

Solution:
1. The given ratio is 10:1, which means for every 1 orange, there are 10 berries.
2. Let the number of berries be \( y \).
3. According to the ratio:
\[
\frac{\text{Berries}}{\text{Oranges}} = \frac{10}{1}
\]
4. Substituting the given number of oranges (25):
\[
\frac{y}{25} = \frac{10}{1}
\]
5. Cross-multiply to solve for \( y \):
\[
y \cdot 1 = 10 \cdot 25 \implies y = 250
\]

Answer: There are 250 berries.

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#### Problem 3:
The ratio of potatoes to turnips is 1:1. If there are 473 potatoes, how many turnips are there?

Solution:
1. The given ratio is 1:1, which means the number of potatoes is equal to the number of turnips.
2. Since there are 473 potatoes, the number of turnips must also be 473.

Answer: There are 473 turnips.

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#### Problem 4:
The ratio of pears to green apples is 1:3. If there are 150 green apples, how many pears are there?

Solution:
1. The given ratio is 1:3, which means for every 1 pear, there are 3 green apples.
2. Let the number of pears be \( z \).
3. According to the ratio:
\[
\frac{\text{Pears}}{\text{Green Apples}} = \frac{1}{3}
\]
4. Substituting the given number of green apples (150):
\[
\frac{z}{150} = \frac{1}{3}
\]
5. Cross-multiply to solve for \( z \):
\[
z \cdot 3 = 1 \cdot 150 \implies 3z = 150 \implies z = \frac{150}{3} = 50
\]

Answer: There are 50 pears.

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#### Problem 5:
The ratio of bananas to melons is 30:1. If there are 300 bananas, how many melons are there?

Solution:
1. The given ratio is 30:1, which means for every 30 bananas, there is 1 melon.
2. Let the number of melons be \( m \).
3. According to the ratio:
\[
\frac{\text{Bananas}}{\text{Melons}} = \frac{30}{1}
\]
4. Substituting the given number of bananas (300):
\[
\frac{300}{m} = \frac{30}{1}
\]
5. Cross-multiply to solve for \( m \):
\[
300 \cdot 1 = 30 \cdot m \implies 300 = 30m \implies m = \frac{300}{30} = 10
\]

Answer: There are 10 melons.

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#### Problem 6:
The ratio of blueberries to strawberries is 1:7. If there are 210 strawberries, how many blueberries are there?

Solution:
1. The given ratio is 1:7, which means for every 1 blueberry, there are 7 strawberries.
2. Let the number of blueberries be \( b \).
3. According to the ratio:
\[
\frac{\text{Blueberries}}{\text{Strawberries}} = \frac{1}{7}
\]
4. Substituting the given number of strawberries (210):
\[
\frac{b}{210} = \frac{1}{7}
\]
5. Cross-multiply to solve for \( b \):
\[
b \cdot 7 = 1 \cdot 210 \implies 7b = 210 \implies b = \frac{210}{7} = 30
\]

Answer: There are 30 blueberries.

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Final Answers:

1. 50 red apples
2. 250 berries
3. 473 turnips
4. 50 pears
5. 10 melons
6. 30 blueberries

\boxed{50, 250, 473, 50, 10, 30}