Flynn, Owen and Jack had some pens in the ratio of 2 : 3 : 5. Jack gave 40% of his pens to Flynn and Owen. As a result, Flynn had the same number of pens as Owen and Jack had 46 fewer pens than Flynn.
- What was the percentage increase in Flynn's pens after receiving from Jack?
- How many pens did Owen have at first?
| Flynn |
Owen |
Jack |
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 Jack gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of pens that Flynn and Owen each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of pens that Flynn had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Flynn's pens after receiving from Jack
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 46
3.5 u - 3 u = 46
0.5 u = 46
1 u = 46 ÷ 0.5 = 92
Number of pens that Owen had at first
= 3 u
= 3 x 92
= 276
Answer(s): (a) 75%; (b) 276
