Let’s solve each problem one by one.
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Problem 1a:
Ratio of pinto to black beans = 1 : 1
That means for every 1 pinto bean, there is 1 black bean → so they are equal in number.
If there are 300 pinto beans, then there are also 300 black beans.
Total beans = 300 + 300 =
600
✔ Check: Ratio 1:1 → half are pinto, half are black → 300 each → total 600. Correct.
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Problem 2a:
Jayden and Caden share $140 in ratio 2 : 5
Total parts = 2 + 5 = 7 parts
Jayden gets 2 out of those 7 parts → so his fraction is
2/7
✔ Check: 2/7 of $140 = (2 × 140)/7 = 280/7 = $40 → Caden gets 5/7 = $100 → total $140. Correct.
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Problem 3a:
Coins: nickels : dimes : quarters = 8 : 1 : 2
Quarters = 30 coins → which correspond to “2” parts in the ratio.
So 1 part = 30 ÷ 2 = 15 coins
Nickels = 8 parts = 8 × 15 = 120
Dimes = 1 part = 1 × 15 = 15
Total nickels and dimes = 120 + 15 =
135
✔ Check: Quarters = 2×15=30 ✔️, Nickels=120, Dimes=15 → total coins = 120+15+30=165 → ratio 8:1:2 holds. Correct.
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Problem 4a:
Girls : Boys = 2 : 4 → simplifies to 1 : 2 (but we can use 2:4 as given)
There are 14 girls → which corresponds to “2” parts
So 1 part = 14 ÷ 2 = 7
Boys = 4 parts = 4 × 7 = 28
Total members = girls + boys = 14 + 28 =
42
✔ Check: 14 girls : 28 boys = 14:28 = 1:2 → same as 2:4 simplified. Total 42. Correct.
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Problem 5a:
Total beans = 550
White beans = 2/5 of 550 = (2 × 550)/5 = 1100/5 = 220
Navy beans = rest = 550 - 220 = 330
Ratio white : navy = 220 : 330
Simplify: divide both by 110 → 2 : 3
✔ Check: 220/550 = 2/5 ✔️, 330/550 = 3/5 ✔️ → ratio 2:3. Correct.
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Problem 6a:
Sophia and Isabella share $117 in ratio 1 : 8
Total parts = 1 + 8 = 9
Sophia gets 1 part out of 9 → fraction =
1/9
✔ Check: 1/9 of $117 = 117 ÷ 9 = $13 → Isabella gets 8/9 = $104 → total $117. Correct.
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Final Answer:
1a. 600
2a. 2/7
3a. 135
4a. 42
5a. 2 : 3
6a. 1/9
Parent Tip: Review the logic above to help your child master the concept of ratio worksheet grade 8.
