Zane, Neave and Paul had some cards in the ratio of 2 : 3 : 5. Paul gave 40% of his cards to Zane and Neave. As a result, Zane had the same number of cards as Neave and Paul had 12 fewer cards than Zane.
- What was the percentage increase in Zane's cards after receiving from Paul?
- How many cards did Neave have at first?
| Zane |
Neave |
Paul |
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 cards that Paul gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of cards that Zane and Neave each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of cards that Zane had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Zane's cards after receiving from Paul
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 12
3.5 u - 3 u = 12
0.5 u = 12
1 u = 12 ÷ 0.5 = 24
Number of cards that Neave had at first
= 3 u
= 3 x 24
= 72
Answer(s): (a) 75%; (b) 72
