Simon and George shared some cards in the ratio of 5 : 7. After both each gave away 104 cards to their brother, the ratio of the number of cards Simon had to the total number of cards left was 1 : 5. How many cards did the two boys have at first?
| |
Simon |
George |
Difference |
| Before |
5x3 =
15 u |
7x3 =
21 u |
2x3 =
6 u |
| Change |
- 104 |
- 104 |
|
| After |
1x2 =
2 u |
4x2 =
8 u |
3x2 =
6 u |
Number of cards that Simon and George each gave to their brother is the same.
The difference in the number of cards at first and in the end between Simon and George remains unchanged. Make the difference in the number of cards the same. LCM of 2 and 3 is 6.
Number of cards that Simon gave to their brother
= 15 u - 2 u
= 13 u
13 u = 104
1 u = 104 ÷ 13 = 8
Number of cards that the two boys had at first
= 15 u + 21 u
= 36 u
= 36 x 8
= 288
Answer(s): 288
