Zane and Usha has some money each. If Usha gives Zane $19, he will have 7 times as much money as her. If Zane gives Usha $15, he will have the same amount of money as her. How much money does each person have respectively?
- Zane?
- Usha?
| |
Case 1 |
Case 2 |
| |
Zane |
Usha |
Zane |
Usha |
| Before |
7 u - 19 |
1 u + 19 |
4 u + 15 |
4 u - 15 |
| Change |
+ 19 |
- 19 |
- 15 |
+ 15 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Usha gives Zane some money or Zane gives Usha some money, the total amount of money remains the same.
Total amount that Zane and Usha have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Zane and Usha each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Zane has at first in Case 1 and Case 2 is the same.
7 u - 19 = 4 u + 15
7 u - 4 u = 15 + 19
1 u = 34
Amount that Zane has
= 4 u + 15
= 4 x 34 + 15
= 136 + 15
= $151
(b)
Amount that Usha has
= 1 u + 19
= 34 + 19
= $53
Answer(s): (a) $151; (b) $53
