Perry and Emma has some money each. If Emma gives Perry $12, he will have 7 times as much money as her. If Perry gives Emma $19, he will have the same amount of money as her. How much money does each person have respectively?
- Perry?
- Emma?
| |
Case 1 |
Case 2 |
| |
Perry |
Emma |
Perry |
Emma |
| Before |
7 u - 12 |
1 u + 12 |
4 u + 19 |
4 u - 19 |
| Change |
+ 12 |
- 12 |
- 19 |
+ 19 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Emma gives Perry some money or Perry gives Emma some money, the total amount of money remains the same.
Total amount that Perry and Emma have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Perry and Emma each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Perry has at first in Case 1 and Case 2 is the same.
7 u - 12 = 4 u + 19
7 u - 4 u = 19 + 12
1 u = 31
Amount that Perry has
= 4 u + 19
= 4 x 31 + 19
= 124 + 19
= $143
(b)
Amount that Emma has
= 1 u + 12
= 31 + 12
= $43
Answer(s): (a) $143; (b) $43
