Xavier and Tammy has some money each. If Tammy gives Xavier $12, he will have 7 times as much money as her. If Xavier gives Tammy $20, he will have the same amount of money as her. How much money does each person have respectively?
- Xavier?
- Tammy?
| |
Case 1 |
Case 2 |
| |
Xavier |
Tammy |
Xavier |
Tammy |
| Before |
7 u - 12 |
1 u + 12 |
4 u + 20 |
4 u - 20 |
| Change |
+ 12 |
- 12 |
- 20 |
+ 20 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Tammy gives Xavier some money or Xavier gives Tammy some money, the total amount of money remains the same.
Total amount that Xavier and Tammy have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Xavier and Tammy each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Xavier has at first in Case 1 and Case 2 is the same.
7 u - 12 = 4 u + 20
7 u - 4 u = 20 + 12
1 u = 32
Amount that Xavier has
= 4 u + 20
= 4 x 32 + 20
= 128 + 20
= $148
(b)
Amount that Tammy has
= 1 u + 12
= 32 + 12
= $44
Answer(s): (a) $148; (b) $44
