Reggie, Sean and Gabriel had a total of 150 marbles. The ratio of the number of marbles that Sean had to the number of marbles that Gabriel had was 4 : 7. After Reggie and Sean each gave away half of their marbles, the 3 children had 117 marbles left. How many marbles did Sean and Gabriel have at first?
| |
Reggie |
Sean |
Gabriel |
Total |
| Before |
2 p |
4 u |
7 u |
150 |
| Change |
- 1 p |
- 2 u |
|
- 33 |
| After |
1 p |
2 u |
7 u |
117 |
Total number of marbles that Reggie and Sean gave away
= 150 - 117
= 33
1 p + 2 u = 33 --- (1)
1 p + 2 u + 7 u = 117
1 p + 9 u = 117 --- (2)
(2) - (1)
(1 p + 9 u) - (1 p + 2 u) = 117 - 33
9 u - 2 u = 84
7 u = 84
1 u = 84 ÷ 7 = 12
Total number of marbles that Sean and Gabriel had at first
= 4 u + 7 u
= 11 u
= 11 x 12
= 132
Answer(s): 132
