Glen, Vincent and Ethan had some pens in the ratio of 2 : 3 : 5. Ethan gave 40% of his pens to Glen and Vincent. As a result, Glen had the same number of pens as Vincent and Ethan had 29 fewer pens than Glen.
- What was the percentage increase in Glen's pens after receiving from Ethan?
- How many pens did Vincent have at first?
| Glen |
Vincent |
Ethan |
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 pens that Ethan gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of pens that Glen and Vincent each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of pens that Glen had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Glen's pens after receiving from Ethan
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 29
3.5 u - 3 u = 29
0.5 u = 29
1 u = 29 ÷ 0.5 = 58
Number of pens that Vincent had at first
= 3 u
= 3 x 58
= 174
Answer(s): (a) 75%; (b) 174
