Sam, Billy and Zeph had some cards in the ratio of 2 : 3 : 5. Zeph gave 40% of his cards to Sam and Billy. As a result, Sam had the same number of cards as Billy and Zeph had 45 fewer cards than Sam.
- What was the percentage increase in Sam's cards after receiving from Zeph?
- How many cards did Billy have at first?
| Sam |
Billy |
Zeph |
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 Zeph gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of cards that Sam and Billy each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of cards that Sam had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Sam's cards after receiving from Zeph
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 45
3.5 u - 3 u = 45
0.5 u = 45
1 u = 45 ÷ 0.5 = 90
Number of cards that Billy had at first
= 3 u
= 3 x 90
= 270
Answer(s): (a) 75%; (b) 270
