Let's solve each problem step by step and explain the reasoning.
---
1 a.
Problem: A jar has 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?
Solution:
- The ratio of pinto to black beans is
1:1, meaning equal amounts.
- Since there are
300 pinto beans, there must also be
300 black beans.
- Total beans = 300 (pinto) + 300 (black) =
600 beans.
✔ Answer: 600 beans
---
2 a.
Problem: Jayden and Caden share a reward of $140 in a ratio of 2:5. What fraction of the total reward does Jayden get?
Solution:
- Ratio = 2:5 → total parts = 2 + 5 =
7 parts
- Jayden gets
2 out of 7 parts
- So, Jayden’s fraction =
2/7
✔ Answer: 2/7
---
3 a.
Problem: 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?
Solution:
- Ratio: Nickels : Dimes : Quarters = 8 : 1 : 2
- Let the common multiplier be
x.
- Then:
- Nickels = 8x
- Dimes = 1x
- Quarters = 2x
We're told that
quarters = 30, so:
> 2x = 30 → x = 15
Now calculate:
- Nickels = 8x = 8 × 15 =
120
- Dimes = 1x = 1 × 15 =
15
✔ Answer: 120 nickels and 15 dimes
---
4 a.
Problem: 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?
Solution:
- Ratio of girls to boys = 2:4 → simplify to
1:2
- But we can use the original ratio: 2 parts girls : 4 parts boys
- Given: 2 parts = 14 girls → so 1 part = 7
- Therefore:
- Girls = 2 × 7 = 14 (matches)
- Boys = 4 × 7 =
28
- Total members = 14 + 28 =
42
✔ Answer: 42 members
---
5 a.
Problem: 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?
Solution:
- Total beans = 550
- White beans = (2/5) × 550 = 220
- Navy beans = 550 – 220 = 330
Now find the ratio of white to navy beans:
> White : Navy = 220 : 330
Simplify the ratio:
- Divide both by 10: 22 : 33
- Divide by 11:
2 : 3
✔ Answer: 2:3
---
6 a.
Problem: Sophia and Isabella share a reward of $117 in a ratio of 1:8. What fraction of the total reward does Sophia get?
Solution:
- Ratio = 1:8 → total parts = 1 + 8 = 9
- Sophia gets 1 part out of 9
- So, her fraction =
1/9
✔ Answer: 1/9
---
✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 1 a | 600 beans |
| 2 a | 2/7 |
| 3 a | 120 nickels and 15 dimes |
| 4 a | 42 members |
| 5 a | 2:3 |
| 6 a | 1/9 |
Let me know if you'd like these explained in simpler terms or with visual models!
Parent Tip: Review the logic above to help your child master the concept of comparing ratios worksheet.
