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