Glen and Jane has some money each. If Jane gives Glen $19, he will have 3 times as much money as her. If Glen gives Jane $18, he will have the same amount of money as her. How much money does each person have respectively?
- Glen?
- Jane?
| |
Case 1 |
Case 2 |
| |
Glen |
Jane |
Glen |
Jane |
| Before |
3 u - 19 |
1 u + 19 |
2 u + 18 |
2 u - 18 |
| Change |
+ 19 |
- 19 |
- 18 |
+ 18 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Jane gives Glen some money or Glen gives Jane some money, the total amount of money remains the same.
Total amount that Glen and Jane have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Glen and Jane each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Glen has at first in Case 1 and Case 2 is the same.
3 u - 19 = 2 u + 18
3 u - 2 u = 18 + 19
1 u = 37
Amount that Glen has
= 2 u + 18
= 2 x 37 + 18
= 74 + 18
= $92
(b)
Amount that Jane has
= 1 u + 19
= 37 + 19
= $56
Answer(s): (a) $92; (b) $56
