Jack, Billy and Dylan had a total of 42 coins. The ratio of the number of coins that Billy had to the number of coins that Dylan had was 2 : 5. After Jack and Billy each gave away half of their coins, the 3 children had 31 coins left. How many coins did Billy and Dylan have in the end?
| |
Jack |
Billy |
Dylan |
Total |
| Before |
2 p |
2 u |
5 u |
42 |
| Change |
- 1 p |
- 1 u |
|
- 11 |
| After |
1 p |
1 u |
5 u |
31 |
Total number of coins that Jack and Billy gave away
= 42 - 31
= 11
1 p + 1 u = 11 --- (1)
1 p + 1 u + 5 u = 31
1 p + 6 u = 31 --- (2)
(2) - (1)
(1 p + 6 u) - (1 p + 1 u) = 31 - 11
6 u - 1 u = 20
5 u = 20
1 u = 20 ÷ 5 = 4
Total number of coins that Billy and Dylan had in the end
= 1 u + 5 u
= 6 u
= 6 x 4
= 24
Answer(s): 24
