Billy, Will and Pierre had some coins in the ratio of 2 : 3 : 5. Pierre gave 40% of his coins to Billy and Will. As a result, Billy had the same number of coins as Will and Pierre had 18 fewer coins than Billy.
- What was the percentage increase in Billy's coins after receiving from Pierre?
- How many coins did Will have at first?
| Billy |
Will |
Pierre |
Total |
| 2 u |
3 u |
5 u |
10 u |
| + 2 u |
- 2 u |
|
| 3.5 u |
3.5 u |
3 u |
10 u |
(a)
Number of coins that Pierre gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of coins that Billy and Will each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of coins that Billy had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Billy's coins after receiving from Pierre
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 18
3.5 u - 3 u = 18
0.5 u = 18
1 u = 18 ÷ 0.5 = 36
Number of coins that Will had at first
= 3 u
= 3 x 36
= 108
Answer(s): (a) 75%; (b) 108
