Jen, Yen and Hilda had a total of 152 marbles. The ratio of Yen's marbles to Hilda's marbles was at first 8 : 7. After Jen and Yen each gave half of their marbles away, the 3 children had 104 marbles left. How many marbles did Jen and Yen have at first?
| |
Jen |
Yen |
Hilda |
Total |
| Before |
2 p |
8 u |
7 u |
152 |
| Change |
- 1 p |
- 4 u |
|
- 48 |
| After |
1 p |
4 u |
7 u |
104 |
Number of marbles that Jen and Yen gave away
= 152 - 104
= 48
1 p + 4 u = 48
1 p = 48 - 4 u --- (1)
1 p + 4 u + 7 u = 104
1 p + 11 u = 104
1 p = 104 - 11 u --- (2)
(1) = (2)
48 - 4 u = 104 - 11 u
11 u - 4 u = 104 - 48
7 u = 56
1 u = 56 ÷ 7 = 8
From (1)
1 p = 48 - 4 u
1 p = 48 - 4 x 8
1 p = 48 - 32 = 16
Number of marbles that Jen and Yen had at first
= 2 p + 8 u
= 2 x 16 + 8 x 8
= 32 + 56
= 88
Answer(s): 88
