Let's solve each of the
Ratio and Rates Word Problems step by step and explain the solutions clearly.
---
1) Are these ratios equivalent?
12 cards to 72 animals vs.
11 marbles to 66 marbles
- First ratio: $ \frac{12}{72} = \frac{1}{6} $
- Second ratio: $ \frac{11}{66} = \frac{1}{6} $
✔ Yes, the ratios are equivalent because both simplify to $ \frac{1}{6} $.
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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?
This is a
proportion problem.
Set up the proportion:
$$
\frac{10 \text{ drinks}}{12 \text{ guests}} = \frac{x \text{ drinks}}{252 \text{ guests}}
$$
Cross-multiply:
$$
10 \times 252 = 12x \\
2520 = 12x \\
x = \frac{2520}{12} = 210
$$
✔ Answer: 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 are required?
This is
identical to #2, so the answer is the same.
✔ Answer: 210 soft drinks
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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?
Find the
unit rate (cost per can):
$$
\text{Cost per can} = \frac{3.40}{5} = 0.68 \text{ dollars}
$$
Now multiply by 35:
$$
35 \times 0.68 = 23.80
$$
✔ Answer: $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?
First, find
rate per hour:
$$
\frac{160 \text{ bagels}}{4 \text{ hours}} = 40 \text{ bagels/hour}
$$
Now, in 16 hours:
$$
40 \times 16 = 640 \text{ bagels}
$$
✔ Answer: 640 bagels; rate = 40 bagels per hour
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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?
Set up the proportion:
$$
\frac{2}{3} = \frac{18}{x}
$$
Cross-multiply:
$$
2x = 54 \Rightarrow x = 27
$$
✔ Answer: 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 are short. Which class has a higher ratio of tall to short students?
- Jack’s class: $ \frac{18}{10} = 1.8 $
- Michael’s class: $ \frac{54}{30} = 1.8 $
✔ Both classes have the same ratio (1.8) — 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?
Calculate
price per apple:
- Quick Market: $ \frac{1.44}{3} = 0.48 $ per apple
- Walmart: $ \frac{2.50}{5} = 0.50 $ per apple
✔ Quick Market is the better buy ($0.48 < $0.50)
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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?
$$
\frac{12}{20} = \frac{3}{5}
$$
✔ Answer: 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?
This is
the same as #5.
- Rate per hour: $ \frac{160}{4} = 40 $ bagels/hour
- In 16 hours: $ 40 \times 16 = 640 $ bagels
✔ Answer: 640 bagels; rate = 40 bagels per hour
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✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1 | Yes, the ratios are equivalent |
| 2 | 210 soft drinks |
| 3 | 210 soft drinks |
| 4 | $23.80 |
| 5 | 640 bagels; 40 bagels/hour |
| 6 | 27 girls |
| 7 | Both classes have the same ratio (1.8) |
| 8 | Quick Market is the better buy |
| 9 | 3:5 |
| 10 | 640 bagels; 40 bagels/hour |
Let me know if you'd like this formatted as a printable worksheet!
Parent Tip: Review the logic above to help your child master the concept of ratio word problems worksheet.
