Hazel, Sarah and Tammy had a total of 46 stamps. The ratio of Sarah's stamps to Tammy's stamps was at first 4 : 3. After Hazel and Sarah each gave half of their stamps away, the 3 children had 26 stamps left. How many stamps did Hazel and Sarah have at first?
| |
Hazel |
Sarah |
Tammy |
Total |
| Before |
2 p |
4 u |
3 u |
46 |
| Change |
- 1 p |
- 2 u |
|
- 20 |
| After |
1 p |
2 u |
3 u |
26 |
Number of stamps that Hazel and Sarah gave away
= 46 - 26
= 20
1 p + 2 u = 20
1 p = 20 - 2 u --- (1)
1 p + 2 u + 3 u = 26
1 p + 5 u = 26
1 p = 26 - 5 u --- (2)
(1) = (2)
20 - 2 u = 26 - 5 u
5 u - 2 u = 26 - 20
3 u = 6
1 u = 6 ÷ 3 = 2
From (1)
1 p = 20 - 2 u
1 p = 20 - 2 x 2
1 p = 20 - 4 = 16
Number of stamps that Hazel and Sarah had at first
= 2 p + 4 u
= 2 x 16 + 4 x 2
= 32 + 6
= 38
Answer(s): 38
