Carl, Sam and Will had some coins in the ratio of 2 : 3 : 5. Will gave 40% of his coins to Carl and Sam. As a result, Carl had the same number of coins as Sam and Will had 27 fewer coins than Carl.
- What was the percentage increase in Carl's coins after receiving from Will?
- How many coins did Sam have at first?
| Carl |
Sam |
Will |
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 coins that Will gave away
= 40% x 5
=
40100 x 5
= 2 u
Number of coins that Carl and Sam each had in the end
= (10 u - 3 u) ÷ 2
= 7 u ÷ 2
= 3.5 u
Increase in the number of coins that Carl had
= 3.5 u - 2 u
= 1.5 u
Percentage increase in Carl's coins after receiving from Will
=
1.52 x 100%
= 75%
(b)
3.5 u = 3 u + 27
3.5 u - 3 u = 27
0.5 u = 27
1 u = 27 ÷ 0.5 = 54
Number of coins that Sam had at first
= 3 u
= 3 x 54
= 162
Answer(s): (a) 75%; (b) 162
