Ethan, Elijah and Justin had some pens in the ratio of 2 : 3 : 5. Justin gave 40% of his pens to Ethan and Elijah. As a result, Ethan had the same number of pens as Elijah and Justin had 16 fewer pens than Ethan.
- What was the percentage increase in Ethan's pens after receiving from Justin?
- How many pens did Elijah have at first?
| Ethan |
Elijah |
Justin |
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 Justin gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of pens that Ethan and Elijah each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of pens that Ethan had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Ethan's pens after receiving from Justin
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 16
3.5 u - 3 u = 16
0.5 u = 16
1 u = 16 ÷ 0.5 = 32
Number of pens that Elijah had at first
= 3 u
= 3 x 32
= 96
Answer(s): (a) 75%; (b) 96
