Anna, Nicole and Wendy had a total of 105 cards. The ratio of Nicole's cards to Wendy's cards was at first 4 : 9. After Anna and Nicole each gave half of their cards away, the 3 children had 75 cards left. How many cards did Anna and Nicole have at first?
| |
Anna |
Nicole |
Wendy |
Total |
| Before |
2 p |
4 u |
9 u |
105 |
| Change |
- 1 p |
- 2 u |
|
- 30 |
| After |
1 p |
2 u |
9 u |
75 |
Number of cards that Anna and Nicole gave away
= 105 - 75
= 30
1 p + 2 u = 30
1 p = 30 - 2 u --- (1)
1 p + 2 u + 9 u = 75
1 p + 11 u = 75
1 p = 75 - 11 u --- (2)
(1) = (2)
30 - 2 u = 75 - 11 u
11 u - 2 u = 75 - 30
9 u = 45
1 u = 45 ÷ 9 = 5
From (1)
1 p = 30 - 2 u
1 p = 30 - 2 x 5
1 p = 30 - 10 = 20
Number of cards that Anna and Nicole had at first
= 2 p + 4 u
= 2 x 20 + 4 x 5
= 40 + 45
= 85
Answer(s): 85
