Ryan and Anna has some money each. If Anna gives Ryan $18, he will have 3 times as much money as her. If Ryan gives Anna $10, he will have the same amount of money as her. How much money does each person have respectively?
- Ryan?
- Anna?
|
Case 1 |
Case 2 |
|
Ryan |
Anna |
Ryan |
Anna |
Before |
3 u - 18 |
1 u + 18 |
2 u + 10 |
2 u - 10 |
Change |
+ 18 |
- 18 |
- 10 |
+ 10 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Anna gives Ryan some money or Ryan gives Anna some money, the total amount of money remains the same.
Total amount that Ryan and Anna have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ryan and Anna each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Ryan has at first in Case 1 and Case 2 is the same.
3 u - 18 = 2 u + 10
3 u - 2 u = 10 + 18
1 u = 28
Amount that Ryan has
= 2 u + 10
= 2 x 28 + 10
= 56 + 10
= $66
(b)
Amount that Anna has
= 1 u + 18
= 28 + 18
= $46
Answer(s): (a) $66; (b) $46