Math worksheet focusing on understanding ratios through ten word problems.

Let's solve each problem step by step and explain the reasoning behind each solution.

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1) A classroom had 25 glue sticks. If the ratio of glue sticks to glue bottles was 5 : 2, how many glue bottles did the classroom have?

Given:
- Ratio of glue sticks to glue bottles = 5:2
- Number of glue sticks = 25

We can set up a proportion:

$$
\frac{5}{2} = \frac{25}{x}
$$

Cross-multiply:

$$
5x = 50 \Rightarrow x = 10
$$

✔ Answer: 10 glue bottles

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2) A student finished 8 of her homework problems in class. If the ratio of problems she finished to problems she still had left was 4 : 1, how many homework problems did she have total?

Given:
- Problems finished = 8
- Ratio (finished : left) = 4:1

Let’s say the number of problems left is $ x $. Then:

$$
\frac{8}{x} = \frac{4}{1} \Rightarrow 8 = 4x \Rightarrow x = 2
$$

So, she had 2 problems left.

Total problems = finished + left = 8 + 2 = 10

✔ Answer: 10 problems

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3) On a Saturday, a library checked out 52 books. If 24 of the books were fiction, what is the ratio of non-fiction books to fiction books checked out?

Given:
- Total books = 52
- Fiction = 24
- Non-fiction = 52 - 24 = 28

Ratio of non-fiction to fiction = $ \frac{28}{24} $

Simplify:

$$
\frac{28}{24} = \frac{7}{6}
$$

✔ Answer: 7:6

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4) A recipe called for the ratio of sugar to flour to be 10 : 3. If you used 70 ounces of sugar, how many ounces of flour would you need to use?

Given:
- Sugar : Flour = 10 : 3
- Sugar used = 70 oz

Set up proportion:

$$
\frac{10}{3} = \frac{70}{x}
$$

Cross-multiply:

$$
10x = 210 \Rightarrow x = 21
$$

✔ Answer: 21 ounces of flour

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5) At a bake sale there were 72 raisin cookies sold. If the ratio of raisin cookies sold to oatmeal cookies sold was 9 : 1, what is the combined amount of raisin and oatmeal cookies sold?

Given:
- Raisin cookies = 72
- Ratio (raisin : oatmeal) = 9:1

Let the number of oatmeal cookies be $ x $. Then:

$$
\frac{72}{x} = \frac{9}{1} \Rightarrow 72 = 9x \Rightarrow x = 8
$$

Oatmeal cookies = 8

Combined = 72 + 8 = 80

✔ Answer: 80 cookies

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6) Kaleb had 136 songs on his MP3 player. If he deleted 56 songs, what is the ratio of songs he kept to songs he deleted?

Given:
- Total songs = 136
- Deleted = 56
- Kept = 136 - 56 = 80

Ratio (kept : deleted) = $ \frac{80}{56} $

Simplify:

$$
\frac{80}{56} = \frac{10}{7}
$$

✔ Answer: 10:7

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7) The ratio of red cars to blue cars in a parking lot was 5 : 3. If there were 40 red cars, how many blue cars were there?

Given:
- Red : Blue = 5:3
- Red cars = 40

Set up proportion:

$$
\frac{5}{3} = \frac{40}{x}
$$

Cross-multiply:

$$
5x = 120 \Rightarrow x = 24
$$

✔ Answer: 24 blue cars

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8) A produce store sold 63 red apples. If the ratio of red apples to green apples sold was 7 : 2, what is the combined amount of red and green apples sold?

Given:
- Red apples = 63
- Ratio (red : green) = 7:2

Let green apples = $ x $

$$
\frac{63}{x} = \frac{7}{2} \Rightarrow 7x = 126 \Rightarrow x = 18
$$

Green apples = 18

Total = 63 + 18 = 81

✔ Answer: 81 apples

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9) For homework, a student had to complete 15 problems total. If she finished 6 problems in class, what is the ratio of problems she still needs to complete to problems that she's already finished?

Given:
- Total = 15
- Finished = 6
- Left = 15 - 6 = 9

Ratio (left : finished) = $ \frac{9}{6} = \frac{3}{2} $

✔ Answer: 3:2

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10) At a farm the ratio of cows to horses was 9 : 2. If there were 72 cows at the farm, how many horses were there?

Given:
- Cows : Horses = 9:2
- Cows = 72

Set up proportion:

$$
\frac{9}{2} = \frac{72}{x}
$$

Cross-multiply:

$$
9x = 144 \Rightarrow x = 16
$$

✔ Answer: 16 horses

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✔ Final Answers:

1. 10
2. 10
3. 7:6
4. 21
5. 80
6. 10:7
7. 24
8. 81
9. 3:2
10. 16

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