Tommy and Jade has some money each. If Jade gives Tommy $20, he will have 3 times as much money as her. If Tommy gives Jade $10, he will have the same amount of money as her. How much money does each person have respectively?
- Tommy?
- Jade?
|
Case 1 |
Case 2 |
|
Tommy |
Jade |
Tommy |
Jade |
Before |
3 u - 20 |
1 u + 20 |
2 u + 10 |
2 u - 10 |
Change |
+ 20 |
- 20 |
- 10 |
+ 10 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Jade gives Tommy some money or Tommy gives Jade some money, the total amount of money remains the same.
Total amount that Tommy and Jade have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Tommy and Jade each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Tommy has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 10
3 u - 2 u = 10 + 20
1 u = 30
Amount that Tommy has
= 2 u + 10
= 2 x 30 + 10
= 60 + 10
= $70
(b)
Amount that Jade has
= 1 u + 20
= 30 + 20
= $50
Answer(s): (a) $70; (b) $50