Lee, Cole and Peter had some coins in the ratio of 3 : 4 : 7. Peter gave 50% of his coins to Lee and Cole. As a result, Lee had the same number of coins as Cole and Peter had 42 fewer coins than Lee.
- What was the percentage increase in Lee's coins after receiving from Peter?
- How many coins did Cole have at first?
| Lee |
Cole |
Peter |
Total |
| 3 u |
4 u |
7 u |
14 u |
| + 3.5 u |
- 3.5 u |
|
| 5.25 u |
5.25 u |
3.5 u |
14 u |
(a)
Number of coins that Peter gave away
= 50% x 7
=
50100 x 7
= 3.5 u
Number of coins that Lee and Cole each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u
Increase in the number of coins that Lee had
= 5.25 u - 3 u
= 2.25 u
Percentage increase in Lee's coins after receiving from Peter
=
2.253 x 100%
= 75%
(b)
5.25 u = 3.5 u + 42
5.25 u - 3.5 u = 42
1.75 u = 42
1 u = 42 ÷ 1.75 = 24
Number of coins that Cole had at first
= 4 u
= 4 x 24
= 96
Answer(s): (a) 75%; (b) 96
