Lee, Valen and Oscar had some pens in the ratio of 6 : 7 : 13. Oscar gave 50% of his pens to Lee and Valen. As a result, Lee had the same number of pens as Valen and Oscar had 26 fewer pens than Lee.
- What was the percentage increase in Lee's pens after receiving from Oscar?
- How many pens did Valen have at first?
| Lee |
Valen |
Oscar |
Total |
| 6 u |
7 u |
13 u |
26 u |
| + 6.5 u |
- 6.5 u |
|
| 9.75 u |
9.75 u |
6.5 u |
26 u |
(a)
Number of pens that Oscar gave away
= 50% x 13
=
50100 x 13
= 6.5 u
Number of pens that Lee and Valen each had in the end
= (26 u - 6.5 u) ÷ 2
= 19.5 u ÷ 2
= 9.75 u
Increase in the number of pens that Lee had
= 9.75 u - 6 u
= 3.75 u
Percentage increase in Lee's pens after receiving from Oscar
=
3.756 x 100%
= 62.5%
(b)
9.75 u = 6.5 u + 26
9.75 u - 6.5 u = 26
3.25 u = 26
1 u = 26 ÷ 3.25 = 8
Number of pens that Valen had at first
= 7 u
= 7 x 8
= 56
Answer(s): (a) 62.5%; (b) 56
