Japheth and Dylan shared some cards in the ratio of 5 : 8. After both each gave away 77 cards to their sister, the ratio of the number of cards Japheth had to the total number of cards left was 1 : 4. How many cards did the two boys have in the end?
|
Japheth |
Dylan |
Difference |
Before |
5x2 = 10 u |
8x2 = 16 u |
3x2 = 6 u |
Change |
- 77 |
- 77 |
|
After |
1x3 = 3 u |
3x3 = 9 u |
2x3 = 6 u |
Number of cards that Japheth and Dylan each gave to their sister is the same.
The difference in the number of cards at first and in the end between Japheth and Dylan remains unchanged. Make the difference in the number of cards the same. LCM of 3 and 2 is 6.
Number of cards that Japheth gave to their sister
= 10 u - 3 u
= 7 u
7 u = 77
1 u = 77 ÷ 7 = 11
Number of cards that the two boys had in the end
= 3 u + 9 u
= 12 u
= 12 x 11
= 132
Answer(s): 132