Billy, Daniel and Caden had a total of 97 coins. The ratio of the number of coins that Daniel had to the number of coins that Caden had was 4 : 7. After Billy and Daniel each gave away half of their coins, the 3 children had 73 coins left. How many coins did Daniel and Caden have in the end?
| |
Billy |
Daniel |
Caden |
Total |
| Before |
2 p |
4 u |
7 u |
97 |
| Change |
- 1 p |
- 2 u |
|
- 24 |
| After |
1 p |
2 u |
7 u |
73 |
Total number of coins that Billy and Daniel gave away
= 97 - 73
= 24
1 p + 2 u = 24 --- (1)
1 p + 2 u + 7 u = 73
1 p + 9 u = 73 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 73 - 24
9 u - 2 u = 49
7 u = 49
1 u = 49 ÷ 7 = 7
Total number of coins that Daniel and Caden had in the end
= 2 u + 7 u
= 9 u
= 9 x 7
= 63
Answer(s): 63
