Betty, Pamela and Jane had a total of 92 marbles. The ratio of Pamela's marbles to Jane's marbles was at first 8 : 7. After Betty and Pamela each gave half of their marbles away, the 3 children had 60 marbles left. How many marbles did Betty and Jane have at first?
| |
Betty |
Pamela |
Jane |
Total |
| Before |
2 p |
8 u |
7 u |
92 |
| Change |
- 1 p |
- 4 u |
|
- 32 |
| After |
1 p |
4 u |
7 u |
60 |
Number of marbles that Betty and Pamela gave away
= 92 - 60
= 32
1 p + 4 u = 32
1 p = 32 - 4 u --- (1)
1 p + 4 u + 7 u = 60
1 p + 11 u = 60
1 p = 60 - 11 u --- (2)
(1) = (2)
32 - 4 u = 60 - 11 u
11 u - 4 u = 60 - 32
7 u = 28
1 u = 28 ÷ 7 = 4
From (1)
1 p = 32 - 4 u
1 p = 32 - 4 x 4
1 p = 32 - 16 = 16
Number of marbles that Betty and Jane had at first
= 2 p + 7 u
= 2 x 16 + 7 x 4
= 32 + 28
= 60
Answer(s): 60
