Sam, Lee and Caden had some pens in the ratio of 2 : 3 : 5. Caden gave 40% of his pens to Sam and Lee. As a result, Sam had the same number of pens as Lee and Caden had 25 fewer pens than Sam.
- What was the percentage increase in Sam's pens after receiving from Caden?
- How many pens did Lee have at first?
| Sam |
Lee |
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 Sam and Lee each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of pens that Sam had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Sam's pens after receiving from Caden
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 25
3.5 u - 3 u = 25
0.5 u = 25
1 u = 25 ÷ 0.5 = 50
Number of pens that Lee had at first
= 3 u
= 3 x 50
= 150
Answer(s): (a) 75%; (b) 150
