Ryan and Abi has some money each. If Abi gives Ryan $11, he will have 3 times as much money as her. If Ryan gives Abi $16, he will have the same amount of money as her. How much money does each person have respectively?
- Ryan?
- Abi?
| |
Case 1 |
Case 2 |
| |
Ryan |
Abi |
Ryan |
Abi |
| Before |
3 u - 11 |
1 u + 11 |
2 u + 16 |
2 u - 16 |
| Change |
+ 11 |
- 11 |
- 16 |
+ 16 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Abi gives Ryan some money or Ryan gives Abi some money, the total amount of money remains the same.
Total amount that Ryan and Abi have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ryan and Abi 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 - 11 = 2 u + 16
3 u - 2 u = 16 + 11
1 u = 27
Amount that Ryan has
= 2 u + 16
= 2 x 27 + 16
= 54 + 16
= $70
(b)
Amount that Abi has
= 1 u + 11
= 27 + 11
= $38
Answer(s): (a) $70; (b) $38
