Vincent and Peter went shopping with a total amount of $270. They had $216 left after shopping. Vincent's remaining money was 3 times the amount he paid for. Peter's remaining money was 5 times the amount he had spent.

1. How much did Peter spend?
2. How much did Peter bring along for shopping?

	Vincent	Peter	Total
Before	4 u	6 p	270
Change	- 1 u	- 1 p	- 54
After	3 u	5 p	216

(a)
Amount that Vincent and Peter spent
= 270 - 216
= $54

Amount that Vincent and Peter spent
= 1 u + 1 p

1 u + 1 p = 54
1 u = 54 - 1 p --- (1)

Amount that Vincent and Peter had left
= 3 u + 5 p 

3 u + 5 p = 216
3 u = 216 - 5 p --- (2)

Make u the same.

(1) _{x 3}
3 u = 162 - 3 p --- (3)

(3) = (2)
162 - 3 p = 216 - 5 p 
5 p - 3 p = 216 - 162

2 p = 54

1 p = 54 ÷ 2 = 27

Amount that Peter spent = $27

(b)
Amount that Peter brought along
= 6 p
= 6 x 27
= $162

Answer(s): (a) $27; (b) $162