Luke and Michael went shopping with a total amount of $448. They had $384 left after shopping. Luke's remaining money was 5 times the amount he paid for. Michael's remaining money was 7 times the amount he had spent.

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

	Luke	Michael	Total
Before	6 u	8 p	448
Change	- 1 u	- 1 p	- 64
After	5 u	7 p	384

(a)
Amount that Luke and Michael spent
= 448 - 384
= $64

Amount that Luke and Michael spent
= 1 u + 1 p

1 u + 1 p = 64
1 u = 64 - 1 p --- (1)

Amount that Luke and Michael had left
= 5 u + 7 p 

5 u + 7 p = 384
5 u = 384 - 7 p --- (2)

Make u the same.

(1) _{x 5}
5 u = 320 - 5 p --- (3)

(3) = (2)
320 - 5 p = 384 - 7 p 
7 p - 5 p = 384 - 320

2 p = 64

1 p = 64 ÷ 2 = 32

Amount that Michael spent = $32

(b)
Amount that Michael brought along
= 8 p
= 8 x 32
= $256

Answer(s): (a) $32; (b) $256