Here's the step-by-step solution to each problem on the “Ratio Problems Worksheet”:
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1 a.
*A jar pinto beans and black beans in a ratio of 1 : 1, and 300 of the beans are pinto beans. How many beans in total are there in the jar?*
- Ratio 1:1 means for every 1 pinto bean, there is 1 black bean → equal numbers.
- If there are 300 pinto beans, then there are also 300 black beans.
- Total beans = 300 + 300 =
600
✔ Answer: 600 beans
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2 a.
*Jayden and Caden share a reward of $140 in a ratio of 2 : 5. What fraction of the total reward does Jayden get?*
- Total parts = 2 + 5 = 7 parts
- Jayden gets 2 out of 7 parts → fraction =
2/7
✔ Answer: 2/7
*(Note: The question asks for the fraction, not the dollar amount, so we stop here.)*
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3 a.
*Gavin has nickels, dimes, and quarters in the ratio of 8 : 1 : 2. If 30 of Gavin’s coins are quarters, how many nickels and dimes does Gavin have?*
- Ratio: nickels : dimes : quarters = 8 : 1 : 2
- Quarters correspond to 2 parts → 2 parts = 30 coins
- So, 1 part = 30 ÷ 2 =
15 coins
- Nickels = 8 parts = 8 × 15 =
120
- Dimes = 1 part = 1 × 15 =
15
✔ Answer: 120 nickels and 15 dimes
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4 a.
*The ratio of girls to boys in a swimming club was 2 : 4. There were 14 girls. How many total members were there in the club?*
- Ratio girls : boys = 2 : 4 → can simplify to 1 : 2, but we’ll use 2:4 as given.
- Girls = 2 parts → 2 parts = 14 → 1 part = 7
- Boys = 4 parts = 4 × 7 = 28
- Total members = girls + boys = 14 + 28 =
42
✔ Answer: 42 total members
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5 a.
*A jar contains 550 beans. Of all the beans, 2/5 are white beans and the rest are navy beans. What is the ratio of white beans to navy beans?*
- White beans = 2/5 of 550 = (2/5) × 550 = 220
- Navy beans = 550 – 220 = 330
- Ratio white : navy = 220 : 330
- Simplify by dividing both by 110 → 220 ÷ 110 = 2; 330 ÷ 110 = 3
- So ratio =
2 : 3
✔ Answer: 2 : 3
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6 a.
*Sophia and Isabella share a reward of $117 in a ratio of 1 : 8. What fraction of the total reward does Sophia get?*
- Total parts = 1 + 8 = 9 parts
- Sophia gets 1 part → fraction =
1/9
✔ Answer: 1/9
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✔ Final Answers Summary:
1a.
600 beans
2a.
2/7
3a.
120 nickels and 15 dimes
4a.
42 total members
5a.
2 : 3
6a.
1/9
Let me know if you’d like these explained with diagrams or real-world analogies!
Parent Tip: Review the logic above to help your child master the concept of ratio worksheet with answers.
