Andy, David and Sam had some coins in the ratio of 3 : 4 : 7. Sam gave 50% of his coins to Andy and David. As a result, Andy had the same number of coins as David and Sam had 42 fewer coins than Andy.
- What was the percentage increase in Andy's coins after receiving from Sam?
- How many coins did David have at first?
| Andy |
David |
Sam |
Total |
| 3 u |
4 u |
7 u |
14 u |
| + 3.5 u |
- 3.5 u |
|
| 5.25 u |
5.25 u |
3.5 u |
14 u |
(a)
Number of coins that Sam gave away
= 50% x 7
=
50100 x 7
= 3.5 u
Number of coins that Andy and David each had in the end
= (14 u - 3.5 u) ÷ 2
= 10.5 u ÷ 2
= 5.25 u
Increase in the number of coins that Andy had
= 5.25 u - 3 u
= 2.25 u
Percentage increase in Andy's coins after receiving from Sam
=
2.253 x 100%
= 75%
(b)
5.25 u = 3.5 u + 42
5.25 u - 3.5 u = 42
1.75 u = 42
1 u = 42 ÷ 1.75 = 24
Number of coins that David had at first
= 4 u
= 4 x 24
= 96
Answer(s): (a) 75%; (b) 96
