Neave and Xylia has some money each. If Xylia gives Neave $11, he will have 7 times as much money as her. If Neave gives Xylia $15, he will have the same amount of money as her. How much money does each person have respectively?
- Neave?
- Xylia?
|
Case 1 |
Case 2 |
|
Neave |
Xylia |
Neave |
Xylia |
Before |
7 u - 11 |
1 u + 11 |
4 u + 15 |
4 u - 15 |
Change |
+ 11 |
- 11 |
- 15 |
+ 15 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Xylia gives Neave some money or Neave gives Xylia some money, the total amount of money remains the same.
Total amount that Neave and Xylia have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Neave and Xylia each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Neave has at first in Case 1 and Case 2 is the same.
7 u - 11 = 4 u + 15
7 u - 4 u = 15 + 11
1 u = 26
Amount that Neave has
= 4 u + 15
= 4 x 26 + 15
= 104 + 15
= $119
(b)
Amount that Xylia has
= 1 u + 11
= 26 + 11
= $37
Answer(s): (a) $119; (b) $37