Daniel and Rael were given some allowances each. If Daniel spent $13 each day and Rael spent $39 each day, Daniel would still have $973 left when Rael spent all his allowance. If Daniel spent $39 each day and Rael spent $13 each day, Daniel would still have $37 left when Rael spent all his allowance.

1. How much allowance did Daniel receive?
2. How much allowance did Rael receive?

	Case 1		Case 2
	Daniel	Rael	Daniel	Rael
Before	1 u + 973	3 u	3 p + 37	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	973	0	37	0

(a)
Simplify the ratio.
13 : 39 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 37 = 1 u + 973
9 u - 1 u = 973 - 37
8 u = 936

1 u = 936 ÷ 8 = 117

Allowance that Daniel received
= 1 u + 973
= 117 + 973
= $1090

(b)
Allowance that Rael received
= 3 u
= 3 x 117
= $351

Answers: (a) $1090; (b) $351