Tommy and Marion has some money each. If Marion gives Tommy $17, he will have 7 times as much money as her. If Tommy gives Marion $19, he will have the same amount of money as her. How much money does each person have respectively?
- Tommy?
- Marion?
| |
Case 1 |
Case 2 |
| |
Tommy |
Marion |
Tommy |
Marion |
| Before |
7 u - 17 |
1 u + 17 |
4 u + 19 |
4 u - 19 |
| Change |
+ 17 |
- 17 |
- 19 |
+ 19 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Marion gives Tommy some money or Tommy gives Marion some money, the total amount of money remains the same.
Total amount that Tommy and Marion have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Tommy and Marion each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Tommy has at first in Case 1 and Case 2 is the same.
7 u - 17 = 4 u + 19
7 u - 4 u = 19 + 17
1 u = 36
Amount that Tommy has
= 4 u + 19
= 4 x 36 + 19
= 144 + 19
= $163
(b)
Amount that Marion has
= 1 u + 17
= 36 + 17
= $53
Answer(s): (a) $163; (b) $53
