Tommy and Caden were given some allowances each. If Tommy spent $10 each day and Caden spent $30 each day, Tommy would still have $2553 left when Caden spent all his allowance. If Tommy spent $30 each day and Caden spent $10 each day, Tommy would still have $73 left when Caden spent all his allowance.

1. How much allowance did Tommy receive?
2. How much allowance did Caden receive?

	Case 1		Case 2
	Tommy	Caden	Tommy	Caden
Before	1 u + 2553	3 u	3 p + 73	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	2553	0	73	0

(a)
Simplify the ratio.
10 : 30 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 73 = 1 u + 2553
9 u - 1 u = 2553 - 73
8 u = 2480

1 u = 2480 ÷ 8 = 310

Allowance that Tommy received
= 1 u + 2553
= 310 + 2553
= $2863

(b)
Allowance that Caden received
= 3 u
= 3 x 310
= $930

Answers: (a) $2863; (b) $930