Dylan, Will and Lee had some pens in the ratio of 4 : 5 : 9. Lee gave 50% of his pens to Dylan and Will. As a result, Dylan had the same number of pens as Will and Lee had 36 fewer pens than Dylan.
- What was the percentage increase in Dylan's pens after receiving from Lee?
- How many pens did Will have at first?
| Dylan |
Will |
Lee |
Total |
| 4 u |
5 u |
9 u |
18 u |
| + 4.5 u |
- 4.5 u |
|
| 6.75 u |
6.75 u |
4.5 u |
18 u |
(a)
Number of pens that Lee gave away
= 50% x 9
=
50100 x 9
= 4.5 u
Number of pens that Dylan and Will each had in the end
= (18 u - 4.5 u) ÷ 2
= 13.5 u ÷ 2
= 6.75 u
Increase in the number of pens that Dylan had
= 6.75 u - 4 u
= 2.75 u
Percentage increase in Dylan's pens after receiving from Lee
=
2.754 x 100%
= 68.75%
(b)
6.75 u = 4.5 u + 36
6.75 u - 4.5 u = 36
2.25 u = 36
1 u = 36 ÷ 2.25 = 16
Number of pens that Will had at first
= 5 u
= 5 x 16
= 80
Answer(s): (a) 68.75%; (b) 80
