Percentages and ratio · Ages 13–14

Three-term ratios and sharing worksheet

Part of: Rates, ratios & proportions

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Percentages and ratio · Ages 13–14

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Name:Date:Score:／48

Write each answer in the space. For word problems, show your working and write a sentence answer.

1.$210 is shared among A, B and C in the ratio 6 : 4 : 4. A gets $, B $ and C $.
Fill in each blank
Answer:
2.a : b = 2 : 4 and b : c = 4 : 5. a : b : c = : :
Fill in each blank
Answer:
3.$245 is shared among A, B and C in the ratio 4 : 2 : 1. A gets $, B $ and C $.
Fill in each blank
Answer:
4.a : b = 8 : 5 and b : c = 6 : 1. a : b : c = : : (simplest whole numbers)
Fill in each blank
Answer:
5.A's and B's money are in the ratio 7 : 4, and A has $9 more than B. A has $ and B has $.
Fill in each blank
Answer:
6.A's, B's and C's savings are in the ratio 8 : 7 : 5, and B has $119. Together they have $
Answer:
7.a : b = 5 : 6 and b : c = 9 : 1. a : b : c = : : (simplest whole numbers)
Fill in each blank
Answer:
8.A's and B's money are in the ratio 6 : 5, and A has $19 more than B. A has $ and B has $.
Fill in each blank
Answer:
9.A's, B's and C's savings are in the ratio 8 : 8 : 4, and B has $168. Together they have $
Answer:
10.Three numbers are in the ratio 8 : 3 : 7, and the largest is 30 more than the smallest. Their sum =
Answer:

13.A club's adult and teenage members are in the ratio 1 : 9, and its teenage and child members 2 : 3. Adults : teenagers : children = : : (simplest whole numbers).
Fill in each blank
Working:
Answer:
14.Three brothers' ages are in the ratio 3 : 5 : 8, and their ages add to 48. How old is the eldest?
Working:
Answer:
15.Chi-keung's and Tsz-hin's stamps are in the ratio 1 : 6, and Tsz-hin's and Ming's 4 : 1. Chi-keung has 10 stamps. How many has Ming?
Working:
Answer:
16.A 340 cm ribbon is cut into three pieces in the ratio 4 : 7 : 9. How much longer is the longest piece than the shortest?
- A. 153 cm
- B. 187 cm
- C. 5 cm
- D. 85 cm
Choose the right answer
Working:
Answer:
17.$3,000 of prize money is shared among three winners in the ratio 3 : 5 : 2. The biggest share is $ and the smallest $.
Fill in each blank
Working:
Answer:
18.$360 is shared among A, B and C in 1 : 2 : 3. Find C's share: put the steps in order.
- A. 360 ÷ 6 = 60
- B. 60 × 3 = 180
- C. 1 + 2 + 3 = 6
Write the letters in the right order
Working:
Answer:

Show the answers and working

Three-term ratios and sharing worksheet: Answers and working

1. 90, 60, 60
6 + 4 + 4 = 14 parts, 210 ÷ 14 = 15 a part: 6 × 15 = 90, 4 × 15 = 60, 4 × 15 = 60.
2. 2, 4, 5
b is 4 in both, so they join straight away: 2 : 4 : 5.
3. 140, 70, 35
4 + 2 + 1 = 7 parts, 245 ÷ 7 = 35 a part: 4 × 35 = 140, 2 × 35 = 70, 1 × 35 = 35.
4. 48, 30, 5
The L.C.M. of b's 5 and 6 is 30: the first ratio times 6, the second times 5, give 48 : 30 : 5 = 48 : 30 : 5.
5. 21, 12
The gap, 7 − 4 parts, is 9, so a part is 3: A has 7 × 3 = 21, B 4 × 3 = 12.
6. 340
B's 7 parts are 119, so a part is 119 ÷ 7 = 17; 20 parts in all make 20 × 17 = 340.
7. 15, 18, 2
The L.C.M. of b's 6 and 9 is 18: the first ratio times 3, the second times 2, give 15 : 18 : 2 = 15 : 18 : 2.
8. 114, 95
The gap, 6 − 5 parts, is 19, so a part is 19: A has 6 × 19 = 114, B 5 × 19 = 95.
9. 420
B's 8 parts are 168, so a part is 168 ÷ 8 = 21; 20 parts in all make 20 × 21 = 420.
10. 108
The largest and smallest are 8 − 3 = 5 parts apart, which is 30, so a part is 6; 18 parts make 18 × 6 = 108.

11. True
a is 1 parts and c is 4: a : c = 1 : 4 = 1 : 4. Keep the order a, then c.
12. B. 5 : 9
The L.C.M. of a's 3 and 5 is 15: b = 10 and c = 18, so b : c = 10 : 18 = 5 : 9.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 2, 18, 27
Teenagers are 9 in one ratio and 2 in the other; make both 18, their L.C.M.: adults 2, children 27, so 2 : 18 : 27 = 2 : 18 : 27.
14. 24 years old
16 parts, 48 ÷ 16 = 3 years a part; the eldest is 8 parts, 8 × 3 = 24.
15. 15 stamps
Make Tsz-hin 12: Chi-keung : Tsz-hin : Ming = 2 : 12 : 3. Chi-keung's 2 parts are 10 stamps, 5 a part, so Ming has 3 × 5 = 15.
16. D. 85 cm
4 + 7 + 9 parts, 17 cm a part; the gap is 9 − 4 = 5 parts, 5 × 17 = 85 cm.
17. 1,500, 600
10 parts, 3000 ÷ 10 = 300 a part. The largest and smallest numbers of parts, each times 300.
18. C → A → B
First the number of parts, then one part's worth, then times C's parts.

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