Ryan and Joelle has some money each. If Joelle gives Ryan $17, he will have 5 times as much money as her. If Ryan gives Joelle $13, he will have the same amount of money as her. How much money does each person have respectively?
- Ryan?
- Joelle?
| |
Case 1 |
Case 2 |
| |
Ryan |
Joelle |
Ryan |
Joelle |
| Before |
5 u - 17 |
1 u + 17 |
3 u + 13 |
3 u - 13 |
| Change |
+ 17 |
- 17 |
- 13 |
+ 13 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Joelle gives Ryan some money or Ryan gives Joelle some money, the total amount of money remains the same.
Total amount that Ryan and Joelle have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Ryan and Joelle each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Ryan has at first in Case 1 and Case 2 is the same.
5 u - 17 = 3 u + 13
5 u - 3 u = 13 + 17
1 u = 30
Amount that Ryan has
= 3 u + 13
= 3 x 30 + 13
= 90 + 13
= $103
(b)
Amount that Joelle has
= 1 u + 17
= 30 + 17
= $47
Answer(s): (a) $103; (b) $47
