Simon, Caden and Liam had a total of 127 cards. The ratio of the number of cards that Caden had to the number of cards that Liam had was 4 : 9. After Simon and Caden each gave away half of their cards, the 3 children had 104 cards left. How many cards did Caden and Liam have in the end?
| |
Simon |
Caden |
Liam |
Total |
| Before |
2 p |
4 u |
9 u |
127 |
| Change |
- 1 p |
- 2 u |
|
- 23 |
| After |
1 p |
2 u |
9 u |
104 |
Total number of cards that Simon and Caden gave away
= 127 - 104
= 23
1 p + 2 u = 23 --- (1)
1 p + 2 u + 9 u = 104
1 p + 11 u = 104 --- (2)
(2) - (1)
(1 p + 11 u) - (1 p + 2 u) = 104 - 23
11 u - 2 u = 81
9 u = 81
1 u = 81 ÷ 9 = 9
Total number of cards that Caden and Liam had in the end
= 2 u + 9 u
= 11 u
= 11 x 9
= 99
Answer(s): 99
