Zeph, Ivan and Wesley had some cards in the ratio of 2 : 3 : 5. Wesley gave 40% of his cards to Zeph and Ivan. As a result, Zeph had the same number of cards as Ivan and Wesley had 44 fewer cards than Zeph.
- What was the percentage increase in Zeph's cards after receiving from Wesley?
- How many cards did Ivan have at first?
| Zeph |
Ivan |
Wesley |
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 Wesley gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of cards that Zeph and Ivan each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of cards that Zeph had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Zeph's cards after receiving from Wesley
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 44
3.5 u - 3 u = 44
0.5 u = 44
1 u = 44 ÷ 0.5 = 88
Number of cards that Ivan had at first
= 3 u
= 3 x 88
= 264
Answer(s): (a) 75%; (b) 264
