Tommy and Lynn has some money each. If Lynn gives Tommy $17, he will have 5 times as much money as her. If Tommy gives Lynn $19, he will have the same amount of money as her. How much money does each person have respectively?
- Tommy?
- Lynn?
|
Case 1 |
Case 2 |
|
Tommy |
Lynn |
Tommy |
Lynn |
Before |
5 u - 17 |
1 u + 17 |
3 u + 19 |
3 u - 19 |
Change |
+ 17 |
- 17 |
- 19 |
+ 19 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Lynn gives Tommy some money or Tommy gives Lynn some money, the total amount of money remains the same.
Total amount that Tommy and Lynn have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Tommy and Lynn each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Tommy has at first in Case 1 and Case 2 is the same.
5 u - 17 = 3 u + 19
5 u - 3 u = 19 + 17
1 u = 36
Amount that Tommy has
= 3 u + 19
= 3 x 36 + 19
= 108 + 19
= $127
(b)
Amount that Lynn has
= 1 u + 17
= 36 + 17
= $53
Answer(s): (a) $127; (b) $53