Riordan and Tim were given some allowances each. If Riordan spent $17 each day and Tim spent $51 each day, Riordan would still have $1794 left when Tim spent all his allowance. If Riordan spent $51 each day and Tim spent $17 each day, Riordan would still have $26 left when Tim spent all his allowance.

1. How much allowance did Riordan receive?
2. How much allowance did Tim receive?

	Case 1		Case 2
	Riordan	Tim	Riordan	Tim
Before	1 u + 1794	3 u	3 p + 26	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1794	0	26	0

(a)
Simplify the ratio.
17 : 51 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 26 = 1 u + 1794
9 u - 1 u = 1794 - 26
8 u = 1768

1 u = 1768 ÷ 8 = 221

Allowance that Riordan received
= 1 u + 1794
= 221 + 1794
= $2015

(b)
Allowance that Tim received
= 3 u
= 3 x 221
= $663

Answers: (a) $2015; (b) $663