Nick, Bobby and Tim had some coins in the ratio of 3 : 4 : 7. Tim gave 50% of his coins to Nick and Bobby. As a result, Nick had the same number of coins as Bobby and Tim had 14 fewer coins than Nick.
- What was the percentage increase in Nick's coins after receiving from Tim?
- How many coins did Bobby have at first?
| Nick |
Bobby |
Tim |
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 Tim gave away
= 50% x 7
=
50100 x 7
= 3.5 u
Number of coins that Nick and Bobby 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 Nick had
= 5.25 u - 3 u
= 2.25 u
Percentage increase in Nick's coins after receiving from Tim
=
2.253 x 100%
= 75%
(b)
5.25 u = 3.5 u + 14
5.25 u - 3.5 u = 14
1.75 u = 14
1 u = 14 ÷ 1.75 = 8
Number of coins that Bobby had at first
= 4 u
= 4 x 8
= 32
Answer(s): (a) 75%; (b) 32
