Gabriel, Tommy and Jeremy had a total of 95 marbles. The ratio of the number of marbles that Tommy had to the number of marbles that Jeremy had was 2 : 5. After Gabriel and Tommy each gave away half of their marbles, the 3 children had 75 marbles left. How many marbles did Tommy and Jeremy have at first?
| |
Gabriel |
Tommy |
Jeremy |
Total |
| Before |
2 p |
2 u |
5 u |
95 |
| Change |
- 1 p |
- 1 u |
|
- 20 |
| After |
1 p |
1 u |
5 u |
75 |
Total number of marbles that Gabriel and Tommy gave away
= 95 - 75
= 20
1 p + 1 u = 20 --- (1)
1 p + 1 u + 5 u = 75
1 p + 6 u = 75 --- (2)
(2) - (1)
(1 p + 6 u) - (1 p + 1 u) = 75 - 20
6 u - 1 u = 55
5 u = 55
1 u = 55 ÷ 5 = 11
Total number of marbles that Tommy and Jeremy had at first
= 2 u + 5 u
= 7 u
= 7 x 11
= 77
Answer(s): 77
