Worksheet with ratio and rate word problems for math practice.

Let’s solve each problem one by one with clear explanations.

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**1) Are these ratios equivalent?
12 cards to 72 animals and 11 marbles to 66 marbles**

✔ Answer: Yes, they are equivalent.

Explanation:
To check if two ratios are equivalent, simplify both to lowest terms.

- First ratio: 12 : 72 → divide both by 12 → 1 : 6
- Second ratio: 11 : 66 → divide both by 11 → 1 : 6

Since both simplify to 1:6, they are equivalent.

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2) In a party, 10 soft drinks are required for every 12 guests. If there are 252 guests, how many soft drinks are required?

✔ Answer: 210 soft drinks

Explanation:
Set up a proportion:

> 10 soft drinks / 12 guests = x soft drinks / 252 guests

Cross-multiply:

> 12x = 10 × 252
> 12x = 2520
> x = 2520 ÷ 12 = 210

So, 210 soft drinks are required.

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3) In a party, 10 soft drinks are required for every 12 guests. If there are 252 guests, how many soft drinks is required?

✔ Answer: 210 soft drinks

Note: This is identical to Problem 2. Same answer.

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4) You can buy 5 cans of green beans at a supermarket for $3.40. How much does it cost to buy 35 cans of green beans?

✔ Answer: $23.80

Explanation:
First, find the cost per can:

> $3.40 ÷ 5 = $0.68 per can

Then multiply by 35:

> 35 × $0.68 = $23.80

Alternatively, use proportion:

> 5 cans → $3.40
> 35 cans → x

> 5/3.40 = 35/x → or better: x = (35/5) × 3.40 = 7 × 3.40 = $23.80

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5) The bakers at a Bakery can make 160 bagels in 4 hours. How many bagels can they bake in 16 hours? What is that rate per hour?

✔ Answer: 640 bagels; rate is 40 bagels per hour

Explanation:

First, find the rate per hour:

> 160 bagels ÷ 4 hours = 40 bagels/hour

Now, for 16 hours:

> 40 × 16 = 640 bagels

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6) The ratio of boys to girls in a class is 2 : 3. If there are 18 boys in the class, how many girls are in that class?

✔ Answer: 27 girls

Explanation:
Ratio boys : girls = 2 : 3

If 2 parts = 18 boys, then 1 part = 18 ÷ 2 = 9

So, 3 parts (girls) = 3 × 9 = 27 girls

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7) In Jack's class, 18 of the students are tall and 10 are short. In Michael's class 54 students are tall and 30 students are short. Which class has a higher ratio of tall to short students?

✔ Answer: Both classes have the same ratio.

Explanation:

Jack’s class: 18 tall : 10 short → simplify by dividing by 2 → 9 : 5

Michael’s class: 54 tall : 30 short → divide by 6 → 9 : 5

Same ratio → neither is higher.

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8) The price of 3 apples at the Quick Market is $1.44. The price of 5 of the same apples at Walmart is $2.50. Which place is the better buy?

✔ Answer: Walmart is the better buy

Explanation:
Find unit price (price per apple).

- Quick Market: $1.44 ÷ 3 = $0.48 per apple
- Walmart: $2.50 ÷ 5 = $0.50 per apple

Wait — Quick Market is cheaper per apple ($0.48 < $0.50)

So actually, Quick Market is the better buy.

✘ Correction: I made an error above.

✔ Final Answer: Quick Market is the better buy

Because $0.48 per apple < $0.50 per apple.

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9) Bob has 12 red cards and 20 green cards. What is the ratio of Bob's red cards to his green cards?

✔ Answer: 3 : 5

Explanation:
Red : Green = 12 : 20

Simplify by dividing both by 4 → 3 : 5

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10) The bakers at a Bakery can make 160 bagels in 4 hours. How many bagels can they bake in 16 hours? What is that rate per hour?

✔ Answer: 640 bagels; rate is 40 bagels per hour

Note: This is identical to Problem 5. Same answer.

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## ✔ Final Answers Summary:

1) Yes, equivalent
2) 210 soft drinks
3) 210 soft drinks
4) $23.80
5) 640 bagels; 40 per hour
6) 27 girls
7) Same ratio (9:5)
8) Quick Market is better buy
9) 3:5
10) 640 bagels; 40 per hour

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