Lynn, Marion and Usha had a total of 71 cards. The ratio of Marion's cards to Usha's cards was at first 4 : 9. After Lynn and Marion each gave half of their cards away, the 3 children had 49 cards left. How many cards did Lynn and Usha have at first?
| |
Lynn |
Marion |
Usha |
Total |
| Before |
2 p |
4 u |
9 u |
71 |
| Change |
- 1 p |
- 2 u |
|
- 22 |
| After |
1 p |
2 u |
9 u |
49 |
Number of cards that Lynn and Marion gave away
= 71 - 49
= 22
1 p + 2 u = 22
1 p = 22 - 2 u --- (1)
1 p + 2 u + 9 u = 49
1 p + 11 u = 49
1 p = 49 - 11 u --- (2)
(1) = (2)
22 - 2 u = 49 - 11 u
11 u - 2 u = 49 - 22
9 u = 27
1 u = 27 ÷ 9 = 3
From (1)
1 p = 22 - 2 u
1 p = 22 - 2 x 3
1 p = 22 - 6 = 16
Number of cards that Lynn and Usha had at first
= 2 p + 9 u
= 2 x 16 + 9 x 3
= 32 + 27
= 59
Answer(s): 59
