Luis, Zeph and Xavier have some buttons. The ratios of their buttons are as follows:
Luis : (Luis + Zeph + Xavier) = 1 : 4
Zeph : (Luis + Xavier) = 1 : 4
Xavier has 35 buttons more than Zeph. In the end, Xavier gives away all he has to Zeph and Luis so that both Zeph and Luis end up with the same number of buttons, how many buttons has Luis received from Xavier?
Zeph |
Xavier |
Luis |
Total |
3x5 |
1x5 |
4x5 |
1x4 |
4x4 |
5x4 |
4 u |
11 u |
5 u |
20 u |
The total number of buttons is repeated. Make the total number of buttons the same. LCM of 4 and 5 is 20.
Number of buttons that Xavier has more than Zeph
= 11 u - 4 u
= 7 u
7 u = 35
1 u = 35 ÷ 7 = 5
|
Zeph |
Xavier |
Luis |
Before |
4 u |
11 u |
5 u |
Change |
+ 6 u |
- 11 u |
+ 5 u |
After |
10 u |
0 u |
10 u |
Number of buttons that Luis has received from Xavier
= 10 u - 5 u
= 5 u
= 5 x 5
= 25
Answer(s): 25