Hilda, Betty and Cathy had a total of 54 cards. The ratio of Betty's cards to Cathy's cards was at first 4 : 9. After Hilda and Betty each gave half of their cards away, the 3 children had 36 cards left. How many cards did Hilda and Betty have at first?
| |
Hilda |
Betty |
Cathy |
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 cards that Hilda and Betty 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 cards that Hilda and Betty had at first
= 2 p + 4 u
= 2 x 14 + 4 x 2
= 28 + 18
= 46
Answer(s): 46
