Lynn, Kathy and Kimberly had a total of 78 cards. The ratio of Kathy's cards to Kimberly's cards was at first 4 : 7. After Lynn and Kathy each gave half of their cards away, the 3 children had 53 cards left. How many cards did Lynn and Kimberly have at first?
| |
Lynn |
Kathy |
Kimberly |
Total |
| Before |
2 p |
4 u |
7 u |
78 |
| Change |
- 1 p |
- 2 u |
|
- 25 |
| After |
1 p |
2 u |
7 u |
53 |
Number of cards that Lynn and Kathy gave away
= 78 - 53
= 25
1 p + 2 u = 25
1 p = 25 - 2 u --- (1)
1 p + 2 u + 7 u = 53
1 p + 9 u = 53
1 p = 53 - 9 u --- (2)
(1) = (2)
25 - 2 u = 53 - 9 u
9 u - 2 u = 53 - 25
7 u = 28
1 u = 28 ÷ 7 = 4
From (1)
1 p = 25 - 2 u
1 p = 25 - 2 x 4
1 p = 25 - 8 = 17
Number of cards that Lynn and Kimberly had at first
= 2 p + 7 u
= 2 x 17 + 7 x 4
= 34 + 28
= 62
Answer(s): 62
