Elijah and Emma has some money each. If Emma gives Elijah $15, he will have 3 times as much money as her. If Elijah gives Emma $18, he will have the same amount of money as her. How much money does each person have respectively?
- Elijah?
- Emma?
|
Case 1 |
Case 2 |
|
Elijah |
Emma |
Elijah |
Emma |
Before |
3 u - 15 |
1 u + 15 |
2 u + 18 |
2 u - 18 |
Change |
+ 15 |
- 15 |
- 18 |
+ 18 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Emma gives Elijah some money or Elijah gives Emma some money, the total amount of money remains the same.
Total amount that Elijah and Emma have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Elijah and Emma each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Elijah has at first in Case 1 and Case 2 is the same.
3 u - 15 = 2 u + 18
3 u - 2 u = 18 + 15
1 u = 33
Amount that Elijah has
= 2 u + 18
= 2 x 33 + 18
= 66 + 18
= $84
(b)
Amount that Emma has
= 1 u + 15
= 33 + 15
= $48
Answer(s): (a) $84; (b) $48