Reggie and Valen went shopping with a total amount of $324. They had $270 left after shopping. Reggie's remaining money was 3 times the amount he paid for. Valen's remaining money was 7 times the amount he had spent.

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

	Reggie	Valen	Total
Before	4 u	8 p	324
Change	- 1 u	- 1 p	- 54
After	3 u	7 p	270

(a)
Amount that Reggie and Valen spent
= 324 - 270
= $54

Amount that Reggie and Valen spent
= 1 u + 1 p

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

Amount that Reggie and Valen had left
= 3 u + 7 p 

3 u + 7 p = 270
3 u = 270 - 7 p --- (2)

Make u the same.

(1) _{x 3}
3 u = 162 - 3 p --- (3)

(3) = (2)
162 - 3 p = 270 - 7 p 
7 p - 3 p = 270 - 162

4 p = 108

1 p = 108 ÷ 4 = 27

Amount that Valen spent = $27

(b)
Amount that Valen brought along
= 8 p
= 8 x 27
= $216

Answer(s): (a) $27; (b) $216