Henry, Fred and Caden had some pens in the ratio of 2 : 3 : 5. Caden gave 40% of his pens to Henry and Fred. As a result, Henry had the same number of pens as Fred and Caden had 23 fewer pens than Henry.
- What was the percentage increase in Henry's pens after receiving from Caden?
- How many pens did Fred have at first?
| Henry |
Fred |
Caden |
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 Caden gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of pens that Henry and Fred each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of pens that Henry had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Henry's pens after receiving from Caden
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 23
3.5 u - 3 u = 23
0.5 u = 23
1 u = 23 ÷ 0.5 = 46
Number of pens that Fred had at first
= 3 u
= 3 x 46
= 138
Answer(s): (a) 75%; (b) 138
