Simon and Jean has some money each. If Jean gives Simon $11, he will have 5 times as much money as her. If Simon gives Jean $19, he will have the same amount of money as her. How much money does each person have respectively?
- Simon?
- Jean?
| |
Case 1 |
Case 2 |
| |
Simon |
Jean |
Simon |
Jean |
| Before |
5 u - 11 |
1 u + 11 |
3 u + 19 |
3 u - 19 |
| Change |
+ 11 |
- 11 |
- 19 |
+ 19 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Jean gives Simon some money or Simon gives Jean some money, the total amount of money remains the same.
Total amount that Simon and Jean have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Simon and Jean each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Simon has at first in Case 1 and Case 2 is the same.
5 u - 11 = 3 u + 19
5 u - 3 u = 19 + 11
1 u = 30
Amount that Simon has
= 3 u + 19
= 3 x 30 + 19
= 90 + 19
= $109
(b)
Amount that Jean has
= 1 u + 11
= 30 + 11
= $41
Answer(s): (a) $109; (b) $41
