Billy, Tommy and George had a total of 95 cards. The ratio of the number of cards that Tommy had to the number of cards that George had was 4 : 9. After Billy and Tommy each gave away half of their cards, the 3 children had 79 cards left. How many cards did Tommy and George have at first?
| |
Billy |
Tommy |
George |
Total |
| Before |
2 p |
4 u |
9 u |
95 |
| Change |
- 1 p |
- 2 u |
|
- 16 |
| After |
1 p |
2 u |
9 u |
79 |
Total number of cards that Billy and Tommy gave away
= 95 - 79
= 16
1 p + 2 u = 16 --- (1)
1 p + 2 u + 9 u = 79
1 p + 11 u = 79 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 2 u) = 79 - 16
11 u - 2 u = 63
9 u = 63
1 u = 63 ÷ 9 = 7
Total number of cards that Tommy and George had at first
= 4 u + 9 u
= 13 u
= 13 x 7
= 91
Answer(s): 91
