Gabriel, Asher and Archie had a total of 449 buttons at first. After a week, the number of Gabriel's buttons became 3 times the number of buttons he had at first. The number of Asher's buttons decreased by 145. Archie had one-quarter as many buttons as he had at first. In the end, the three boys had the same number of buttons.
- How many buttons did Archie have at first?
- What was the total number of buttons that the three boys had in the end?
|
Gabriel |
Asher |
Archie |
Total |
Before |
1 u |
3 u + 145 |
12 u |
|
Change |
x 3 |
- 145 |
x 14 |
|
After |
3 u |
3 u |
3 u |
9 u |
(a)
Total number of buttons at first
=
1 u + 3 u + 145 + 12 u
= 16 u + 145
16 u + 145 = 44916 u = 449 - 14516 u = 304
1 u = 304 ÷ 16 = 19 Number of buttons that Archie had at first
= 3 u ÷
14= 3 u x
41= 12 u = 12 x 19 = 228(b)Total number of buttons that the three boys had at the end = 9 u = 9 x 19 = 171 Answer(s): (a) 228; (b) 171