Reggie, Carl and Fred had a total of 113 marbles. The ratio of the number of marbles that Carl had to the number of marbles that Fred had was 4 : 7. After Reggie and Carl each gave away half of their marbles, the 3 children had 88 marbles left. How many marbles did Carl and Fred have at first?
| |
Reggie |
Carl |
Fred |
Total |
| Before |
2 p |
4 u |
7 u |
113 |
| Change |
- 1 p |
- 2 u |
|
- 25 |
| After |
1 p |
2 u |
7 u |
88 |
Total number of marbles that Reggie and Carl gave away
= 113 - 88
= 25
1 p + 2 u = 25 --- (1)
1 p + 2 u + 7 u = 88
1 p + 9 u = 88 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 88 - 25
9 u - 2 u = 63
7 u = 63
1 u = 63 ÷ 7 = 9
Total number of marbles that Carl and Fred had at first
= 4 u + 7 u
= 11 u
= 11 x 9
= 99
Answer(s): 99
