Xavier and Jean has some money each. If Jean gives Xavier $16, he will have 7 times as much money as her. If Xavier gives Jean $10, he will have the same amount of money as her. How much money does each person have respectively?
- Xavier?
- Jean?
| |
Case 1 |
Case 2 |
| |
Xavier |
Jean |
Xavier |
Jean |
| Before |
7 u - 16 |
1 u + 16 |
4 u + 10 |
4 u - 10 |
| Change |
+ 16 |
- 16 |
- 10 |
+ 10 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Jean gives Xavier some money or Xavier gives Jean some money, the total amount of money remains the same.
Total amount that Xavier and Jean have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Xavier and Jean 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 - 16 = 4 u + 10
7 u - 4 u = 10 + 16
1 u = 26
Amount that Xavier has
= 4 u + 10
= 4 x 26 + 10
= 104 + 10
= $114
(b)
Amount that Jean has
= 1 u + 16
= 26 + 16
= $42
Answer(s): (a) $114; (b) $42
