Cole and Natalie has some money each. If Natalie gives Cole $17, he will have 3 times as much money as her. If Cole gives Natalie $11, he will have the same amount of money as her. How much money does each person have respectively?
- Cole?
- Natalie?
| |
Case 1 |
Case 2 |
| |
Cole |
Natalie |
Cole |
Natalie |
| Before |
3 u - 17 |
1 u + 17 |
2 u + 11 |
2 u - 11 |
| Change |
+ 17 |
- 17 |
- 11 |
+ 11 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Natalie gives Cole some money or Cole gives Natalie some money, the total amount of money remains the same.
Total amount that Cole and Natalie have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Cole and Natalie each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Cole has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 11
3 u - 2 u = 11 + 17
1 u = 28
Amount that Cole has
= 2 u + 11
= 2 x 28 + 11
= 56 + 11
= $67
(b)
Amount that Natalie has
= 1 u + 17
= 28 + 17
= $45
Answer(s): (a) $67; (b) $45
