Billy and Valen shared some buttons in the ratio of 5 : 7. After both each gave away 130 buttons to their cousin, the ratio of the number of buttons Billy had to the total number of buttons left was 1 : 5. How many buttons did the two boys have in the end?
|
Billy |
Valen |
Difference |
Before |
5x3 = 15 u |
7x3 = 21 u |
2x3 = 6 u |
Change |
- 130 |
- 130 |
|
After |
1x2 = 2 u |
4x2 = 8 u |
3x2 = 6 u |
Number of buttons that Billy and Valen each gave to their cousin is the same.
The difference in the number of buttons at first and in the end between Billy and Valen remains unchanged. Make the difference in the number of buttons the same. LCM of 2 and 3 is 6.
Number of buttons that Billy gave to their cousin
= 15 u - 2 u
= 13 u
13 u = 130
1 u = 130 ÷ 13 = 10
Number of buttons that the two boys had in the end
= 2 u + 8 u
= 10 u
= 10 x 10
= 100
Answer(s): 100