Sam, John and Andy had some cards in the ratio of 5 : 6 : 11. Andy gave 50% of his cards to Sam and John. As a result, Sam had the same number of cards as John and Andy had 33 fewer cards than Sam.
- What was the percentage increase in Sam's cards after receiving from Andy?
- How many cards did John have at first?
| Sam |
John |
Andy |
Total |
| 5 u |
6 u |
11 u |
22 u |
| + 5.5 u |
- 5.5 u |
|
| 8.25 u |
8.25 u |
5.5 u |
22 u |
(a)
Number of cards that Andy gave away
= 50% x 11
=
50100 x 11
= 5.5 u
Number of cards that Sam and John each had in the end
= (22 u - 5.5 u) ÷ 2
= 16.5 u ÷ 2
= 8.25 u
Increase in the number of cards that Sam had
= 8.25 u - 5 u
= 3.25 u
Percentage increase in Sam's cards after receiving from Andy
=
3.255 x 100%
= 65%
(b)
8.25 u = 5.5 u + 33
8.25 u - 5.5 u = 33
2.75 u = 33
1 u = 33 ÷ 2.75 = 12
Number of cards that John had at first
= 6 u
= 6 x 12
= 72
Answer(s): (a) 65%; (b) 72
