Daniel, Zeph and Mark have some buttons. The ratios of their buttons are as follows:
Daniel : (Daniel + Zeph + Mark) = 2 : 5
Zeph : (Daniel + Mark) = 1 : 5
Mark has 80 buttons more than Zeph. In the end, Mark gives away all he has to Zeph and Daniel so that both Zeph and Daniel end up with the same number of buttons, how many buttons has Daniel received from Mark?
Zeph |
Mark |
Daniel |
Total |
3x6 |
2x6 |
5x6 |
1x5 |
5x5 |
6x5 |
5 u |
13 u |
12 u |
30 u |
The total number of buttons is repeated. Make the total number of buttons the same. LCM of 5 and 6 is 30.
Number of buttons that Mark has more than Zeph
= 13 u - 5 u
= 8 u
8 u = 80
1 u = 80 ÷ 8 = 10
|
Zeph |
Mark |
Daniel |
Before |
5 u |
13 u |
12 u |
Change |
+ 10 u |
- 13 u |
+ 3 u |
After |
15 u |
0 u |
15 u |
Number of buttons that Daniel has received from Mark
= 15 u - 12 u
= 3 u
= 3 x 10
= 30
Answer(s): 30