Japheth and Billy shared some stamps in the ratio of 5 : 7. After both each gave away 30 stamps to their brother, the ratio of the number of stamps Japheth had to the total number of stamps left was 1 : 3. How many stamps did the two boys have at first?
|
Japheth |
Billy |
Difference |
Before |
5x1 = 5 u |
7x1 = 7 u |
2x1 = 2 u |
Change |
- 30 |
- 30 |
|
After |
1x2 = 2 u |
2x2 = 4 u |
1x2 = 2 u |
Number of stamps that Japheth and Billy each gave to their brother is the same.
The difference in the number of stamps at first and in the end between Japheth and Billy remains unchanged. Make the difference in the number of stamps the same. LCM of 2 and 1 is 2.
Number of stamps that Japheth gave to their brother
= 5 u - 2 u
= 3 u
3 u = 30
1 u = 30 ÷ 3 = 10
Number of stamps that the two boys had at first
= 5 u + 7 u
= 12 u
= 12 x 10
= 120
Answer(s): 120