Zane and Abi has some money each. If Abi gives Zane $17, he will have 5 times as much money as her. If Zane gives Abi $11, he will have the same amount of money as her. How much money does each person have respectively?
- Zane?
- Abi?
| |
Case 1 |
Case 2 |
| |
Zane |
Abi |
Zane |
Abi |
| Before |
5 u - 17 |
1 u + 17 |
3 u + 11 |
3 u - 11 |
| Change |
+ 17 |
- 17 |
- 11 |
+ 11 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Abi gives Zane some money or Zane gives Abi some money, the total amount of money remains the same.
Total amount that Zane and Abi have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Zane and Abi each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Zane has at first in Case 1 and Case 2 is the same.
5 u - 17 = 3 u + 11
5 u - 3 u = 11 + 17
1 u = 28
Amount that Zane has
= 3 u + 11
= 3 x 28 + 11
= 84 + 11
= $95
(b)
Amount that Abi has
= 1 u + 17
= 28 + 17
= $45
Answer(s): (a) $95; (b) $45
