Ethan, Jeremy and Sam had some coins in the ratio of 2 : 3 : 5. Sam gave 40% of his coins to Ethan and Jeremy. As a result, Ethan had the same number of coins as Jeremy and Sam had 20 fewer coins than Ethan.
- What was the percentage increase in Ethan's coins after receiving from Sam?
- How many coins did Jeremy have at first?
| Ethan |
Jeremy |
Sam |
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 Sam gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of coins that Ethan and Jeremy each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of coins that Ethan had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Ethan's coins after receiving from Sam
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 20
3.5 u - 3 u = 20
0.5 u = 20
1 u = 20 ÷ 0.5 = 40
Number of coins that Jeremy had at first
= 3 u
= 3 x 40
= 120
Answer(s): (a) 75%; (b) 120
