Fred and Henry shared some cards in the ratio of 5 : 8. After both each gave away 56 cards to their sister, the ratio of the number of cards Fred had to the total number of cards left was 1 : 4. How many cards did the two boys have at first?
| |
Fred |
Henry |
Difference |
| Before |
5x2 =
10 u |
8x2 =
16 u |
3x2 =
6 u |
| Change |
- 56 |
- 56 |
|
| After |
1x3 =
3 u |
3x3 =
9 u |
2x3 =
6 u |
Number of cards that Fred and Henry each gave to their sister is the same.
The difference in the number of cards at first and in the end between Fred and Henry remains unchanged. Make the difference in the number of cards the same. LCM of 3 and 2 is 6.
Number of cards that Fred gave to their sister
= 10 u - 3 u
= 7 u
7 u = 56
1 u = 56 ÷ 7 = 8
Number of cards that the two boys had at first
= 10 u + 16 u
= 26 u
= 26 x 8
= 208
Answer(s): 208
