Dana, Julie and Gem had a total of 54 beads. The ratio of Julie's beads to Gem's beads was at first 4 : 9. After Dana and Julie each gave half of their beads away, the 3 children had 36 beads left. How many beads did Dana and Gem have at first?
| |
Dana |
Julie |
Gem |
Total |
| Before |
2 p |
4 u |
9 u |
54 |
| Change |
- 1 p |
- 2 u |
|
- 18 |
| After |
1 p |
2 u |
9 u |
36 |
Number of beads that Dana and Julie gave away
= 54 - 36
= 18
1 p + 2 u = 18
1 p = 18 - 2 u --- (1)
1 p + 2 u + 9 u = 36
1 p + 11 u = 36
1 p = 36 - 11 u --- (2)
(1) = (2)
18 - 2 u = 36 - 11 u
11 u - 2 u = 36 - 18
9 u = 18
1 u = 18 ÷ 9 = 2
From (1)
1 p = 18 - 2 u
1 p = 18 - 2 x 2
1 p = 18 - 4 = 14
Number of beads that Dana and Gem had at first
= 2 p + 9 u
= 2 x 14 + 9 x 2
= 28 + 18
= 46
Answer(s): 46
