Ivory, Gem and Olivia had a total of 74 stickers. The ratio of Gem's stickers to Olivia's stickers was at first 8 : 9. After Ivory and Gem each gave half of their stickers away, the 3 children had 46 stickers left. How many stickers did Ivory and Gem have at first?
| |
Ivory |
Gem |
Olivia |
Total |
| Before |
2 p |
8 u |
9 u |
74 |
| Change |
- 1 p |
- 4 u |
|
- 28 |
| After |
1 p |
4 u |
9 u |
46 |
Number of stickers that Ivory and Gem gave away
= 74 - 46
= 28
1 p + 4 u = 28
1 p = 28 - 4 u --- (1)
1 p + 4 u + 9 u = 46
1 p + 13 u = 46
1 p = 46 - 13 u --- (2)
(1) = (2)
28 - 4 u = 46 - 13 u
13 u - 4 u = 46 - 28
9 u = 18
1 u = 18 ÷ 9 = 2
From (1)
1 p = 28 - 4 u
1 p = 28 - 4 x 2
1 p = 28 - 8 = 20
Number of stickers that Ivory and Gem had at first
= 2 p + 8 u
= 2 x 20 + 8 x 2
= 40 + 18
= 58
Answer(s): 58
