Luke and Eva has some money each. If Eva gives Luke $10, he will have 7 times as much money as her. If Luke gives Eva $19, he will have the same amount of money as her. How much money does each person have respectively?
- Luke?
- Eva?
|
Case 1 |
Case 2 |
|
Luke |
Eva |
Luke |
Eva |
Before |
7 u - 10 |
1 u + 10 |
4 u + 19 |
4 u - 19 |
Change |
+ 10 |
- 10 |
- 19 |
+ 19 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Eva gives Luke some money or Luke gives Eva some money, the total amount of money remains the same.
Total amount that Luke and Eva have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Luke and Eva each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Luke has at first in Case 1 and Case 2 is the same.
7 u - 10 = 4 u + 19
7 u - 4 u = 19 + 10
1 u = 29
Amount that Luke has
= 4 u + 19
= 4 x 29 + 19
= 116 + 19
= $135
(b)
Amount that Eva has
= 1 u + 10
= 29 + 10
= $39
Answer(s): (a) $135; (b) $39