Nick, Tim and Ryan had some buttons in the ratio of 2 : 3 : 5. Ryan gave 40% of his buttons to Nick and Tim. As a result, Nick had the same number of buttons as Tim and Ryan had 23 fewer buttons than Nick.
- What was the percentage increase in Nick's buttons after receiving from Ryan?
- How many buttons did Tim have at first?
| Nick |
Tim |
Ryan |
Total |
| 2 u |
3 u |
5 u |
10 u |
| + 2 u |
- 2 u |
|
| 3.5 u |
3.5 u |
3 u |
10 u |
(a)
Number of buttons that Ryan gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of buttons that Nick and Tim each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of buttons that Nick had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Nick's buttons after receiving from Ryan
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 23
3.5 u - 3 u = 23
0.5 u = 23
1 u = 23 ÷ 0.5 = 46
Number of buttons that Tim had at first
= 3 u
= 3 x 46
= 138
Answer(s): (a) 75%; (b) 138
