Japheth and Perry were given some allowances each. If Japheth spent $28 each day and Perry spent $84 each day, Japheth would still have $1405 left when Perry spent all his allowance. If Japheth spent $84 each day and Perry spent $28 each day, Japheth would still have $61 left when Perry spent all his allowance.

1. How much allowance did Japheth receive?
2. How much allowance did Perry receive?

	Case 1		Case 2
	Japheth	Perry	Japheth	Perry
Before	1 u + 1405	3 u	3 p + 61	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1405	0	61	0

(a)
Simplify the ratio.
28 : 84 = 1 : 3

The allowance that Perry had at first is the same for Case 1 and Case 2.

1 p = 3 u
3 p = 9 u

The allowance that Japheth had at first is the same for Case 1 and Case 2.

9 u + 61 = 1 u + 1405
9 u - 1 u = 1405 - 61
8 u = 1344

1 u = 1344 ÷ 8 = 168

Allowance that Japheth received
= 1 u + 1405
= 168 + 1405
= $1573

(b)
Allowance that Perry received
= 3 u
= 3 x 168
= $504

Answers: (a) $1573; (b) $504