$240 is shared among A, B and C in the ratio 3 : 2 : 3. A gets $□, B $□ and C $□. Fill in each blank

90, 60, 90. 3 + 2 + 3 = 8 parts, 240 ÷ 8 = 30 a part: 3 × 30 = 90, 2 × 30 = 60, 3 × 30 = 90.

A's, B's and C's savings are in the ratio 8 : 6 : 5, and B has $180. Together they have $□

570. B's 6 parts are 180, so a part is 180 ÷ 6 = 30; 19 parts in all make 19 × 30 = 570.

a : b = 3 : 4 and a : c = 6 : 5. What is b : c? A. 5 : 8 B. 4 : 5 C. 8 : 5 D. 8 : 13 Choose the right answer

C. 8 : 5. The L.C.M. of a's 3 and 6 is 6: b = 8 and c = 5, so b : c = 8 : 5 = 8 : 5.

Rates, ratios & proportions · Ages 13–14

Three-term ratios and sharing

Make the shared term the same, then join the ratios.

How to do it

Method

Make the shared term the same, then join the ratios

a : b = 8 : 12, b : c = 12 : 15, a : b : c = 8 : 12 : 15

Another way

Give the shared term a value

b = 12: a = 12 × 23 = 8, c = 12 × 54 = 15

In full

Given a : b = 2 : 3 and b : c = 4 : 5, find a : b : c. Both ratios hold b, so make b the same number in both: the L.C.M. of 3 and 4 is 12, the first ratio times 4 is 8 : 12, the second times 3 is 12 : 15, so a : b : c = 8 : 12 : 15. Another way: let the shared term b be 12. Then a = 12 × 23 = 8 and c = 12 × 54 = 15, the same. Sharing in a ratio: $700 in 2 : 3 : 5 is 2 + 3 + 5 = 10 parts, a part 700 ÷ 10 = $70, so the shares are $140, $210 and $350; or with fractions, the first is 700 × 210 = $140. Given one share (or the gap between two), find one part first, then multiply back.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
$240 is shared among A, B and C in the ratio 3 : 2 : 3. A gets $, B $ and C $.
Fill in each blank
Show the answer and working
Answer: 90, 60, 90
3 + 2 + 3 = 8 parts, 240 ÷ 8 = 30 a part: 3 × 30 = 90, 2 × 30 = 60, 3 × 30 = 90.
Example 2
A's, B's and C's savings are in the ratio 8 : 6 : 5, and B has $180. Together they have $
Show the answer and working
Answer: 570
B's 6 parts are 180, so a part is 180 ÷ 6 = 30; 19 parts in all make 19 × 30 = 570.
Example 3
a : b = 3 : 4 and a : c = 6 : 5. What is b : c?
- A. 5 : 8
- B. 4 : 5
- C. 8 : 5
- D. 8 : 13
Choose the right answer
Show the answer and working
Answer: C. 8 : 5
The L.C.M. of a's 3 and 6 is 6: b = 8 and c = 5, so b : c = 8 : 5 = 8 : 5.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.a : b = 9 : 8 and b : c = 8 : 5. a : b : c = : :
Fill in each blank
Answer:
2.a : b : c = 2 : 5 : 7, so a : c = 7 : 2.
True or false?
Answer:
3.A's, B's and C's savings are in the ratio 6 : 8 : 4, and B has $96. Together they have $
Answer:
4.a : b = 7 : 6 and a : c = 5 : 6. What is b : c?
- A. 5 : 12
- B. 1 : 1
- C. 5 : 7
- D. 7 : 5
Choose the right answer
Answer:
5.Three numbers are in the ratio 6 : 9 : 5, and the largest is 24 more than the smallest. Their sum =
Answer:

All the answers

1. 9, 8, 5
2. False
3. 216
4. C. 5 : 7
5. 120

Free worksheet: Three-term ratios and sharingWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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