Elijah and Lynn has some money each. If Lynn gives Elijah $17, he will have 7 times as much money as her. If Elijah gives Lynn $15, he will have the same amount of money as her. How much money does each person have respectively?
- Elijah?
- Lynn?
| |
Case 1 |
Case 2 |
| |
Elijah |
Lynn |
Elijah |
Lynn |
| Before |
7 u - 17 |
1 u + 17 |
4 u + 15 |
4 u - 15 |
| Change |
+ 17 |
- 17 |
- 15 |
+ 15 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Lynn gives Elijah some money or Elijah gives Lynn some money, the total amount of money remains the same.
Total amount that Elijah and Lynn have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Elijah and Lynn each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Elijah has at first in Case 1 and Case 2 is the same.
7 u - 17 = 4 u + 15
7 u - 4 u = 15 + 17
1 u = 32
Amount that Elijah has
= 4 u + 15
= 4 x 32 + 15
= 128 + 15
= $143
(b)
Amount that Lynn has
= 1 u + 17
= 32 + 17
= $49
Answer(s): (a) $143; (b) $49
