Brandon and Rachel has some money each. If Rachel gives Brandon $12, he will have 3 times as much money as her. If Brandon gives Rachel $19, he will have the same amount of money as her. How much money does each person have respectively?
- Brandon?
- Rachel?
| |
Case 1 |
Case 2 |
| |
Brandon |
Rachel |
Brandon |
Rachel |
| Before |
3 u - 12 |
1 u + 12 |
2 u + 19 |
2 u - 19 |
| Change |
+ 12 |
- 12 |
- 19 |
+ 19 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Rachel gives Brandon some money or Brandon gives Rachel some money, the total amount of money remains the same.
Total amount that Brandon and Rachel have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Brandon and Rachel each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Brandon has at first in Case 1 and Case 2 is the same.
3 u - 12 = 2 u + 19
3 u - 2 u = 19 + 12
1 u = 31
Amount that Brandon has
= 2 u + 19
= 2 x 31 + 19
= 62 + 19
= $81
(b)
Amount that Rachel has
= 1 u + 12
= 31 + 12
= $43
Answer(s): (a) $81; (b) $43
