Julian and Henry were given some allowances each. If Julian spent $29 each day and Henry spent $58 each day, Julian would still have $442 left when Henry spent all his allowance. If Julian spent $58 each day and Henry spent $29 each day, Julian would still have $94 left when Henry spent all his allowance.

1. How much allowance did Julian receive?
2. How much allowance did Henry receive?

	Case 1		Case 2
	Julian	Henry	Julian	Henry
Before	1 u + 442	2 u	2 p + 94	1 p
Change	- 1 u	- 2 u	- 2 p	- 1 p
After	442	0	94	0

(a)
Simplify the ratio.
29 : 58 = 1 : 2

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

1 p = 2 u
2 p = 4 u

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

4 u + 94 = 1 u + 442
4 u - 1 u = 442 - 94
3 u = 348

1 u = 348 ÷ 3 = 116

Allowance that Julian received
= 1 u + 442
= 116 + 442
= $558

(b)
Allowance that Henry received
= 2 u
= 2 x 116
= $232

Answers: (a) $558; (b) $232