Justin and Ethan went shopping with a total amount of $234. They had $198 left after shopping. Justin's remaining money was 4 times the amount he paid for. Ethan's remaining money was 7 times the amount he had spent.
- How much did Ethan spend?
- How much did Ethan bring along for shopping?
|
Justin |
Ethan |
Total |
Before |
5 u |
8 p |
234 |
Change |
- 1 u |
- 1 p |
- 36 |
After |
4 u |
7 p |
198 |
(a)
Amount that Justin and Ethan spent
= 234 - 198
= $36
Amount that Justin and Ethan spent
= 1 u + 1 p
1 u + 1 p = 36
1 u = 36 - 1 p --- (1)
Amount that Justin and Ethan had left
= 4 u + 7 p
4 u + 7 p = 198
4 u = 198 - 7 p --- (2)
Make u the same.
(1)
x 4 4 u = 144 - 4 p --- (3)
(3) = (2)
144 - 4 p = 198 - 7 p
7 p - 4 p = 198 - 144
3 p = 54
1 p = 54 ÷ 3 = 18
Amount that Ethan spent = $18
(b)
Amount that Ethan brought along
= 8 p
= 8 x 18
= $144
Answer(s): (a) $18; (b) $144