Ivan and Michael went shopping with a total amount of $507. They had $429 left after shopping. Ivan's remaining money was 4 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?

	Ivan	Michael	Total
Before	5 u	8 p	507
Change	- 1 u	- 1 p	- 78
After	4 u	7 p	429

(a)
Amount that Ivan and Michael spent
= 507 - 429
= $78

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

1 u + 1 p = 78
1 u = 78 - 1 p --- (1)

Amount that Ivan and Michael had left
= 4 u + 7 p 

4 u + 7 p = 429
4 u = 429 - 7 p --- (2)

Make u the same.

(1) _{x 4}
4 u = 312 - 4 p --- (3)

(3) = (2)
312 - 4 p = 429 - 7 p 
7 p - 4 p = 429 - 312

3 p = 117

1 p = 117 ÷ 3 = 39

Amount that Michael spent = $39

(b)
Amount that Michael brought along
= 8 p
= 8 x 39
= $312

Answer(s): (a) $39; (b) $312