Fred, Ken and Ethan had some pens in the ratio of 3 : 4 : 7. Ethan gave 50% of his pens to Fred and Ken. As a result, Fred had the same number of pens as Ken and Ethan had 28 fewer pens than Fred.
- What was the percentage increase in Fred's pens after receiving from Ethan?
- How many pens did Ken have at first?
| Fred |
Ken |
Ethan |
Total |
| 3 u |
4 u |
7 u |
14 u |
| + 3.5 u |
- 3.5 u |
|
| 5.25 u |
5.25 u |
3.5 u |
14 u |
(a)
Number of pens that Ethan gave away
= 50% x 7
=
50100 x 7
= 3.5 u
Number of pens that Fred and Ken each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u
Increase in the number of pens that Fred had
= 5.25 u - 3 u
= 2.25 u
Percentage increase in Fred's pens after receiving from Ethan
=
2.253 x 100%
= 75%
(b)
5.25 u = 3.5 u + 28
5.25 u - 3.5 u = 28
1.75 u = 28
1 u = 28 ÷ 1.75 = 16
Number of pens that Ken had at first
= 4 u
= 4 x 16
= 64
Answer(s): (a) 75%; (b) 64
