Brandon and Albert were given some allowances each. If Brandon spent $29 each day and Albert spent $87 each day, Brandon would still have $1901 left when Albert spent all his allowance. If Brandon spent $87 each day and Albert spent $29 each day, Brandon would still have $45 left when Albert spent all his allowance.

1. How much allowance did Brandon receive?
2. How much allowance did Albert receive?

	Case 1		Case 2
	Brandon	Albert	Brandon	Albert
Before	1 u + 1901	3 u	3 p + 45	1 p
Change	- 1 u	- 3 u	- 3 p	- 1 p
After	1901	0	45	0

(a)
Simplify the ratio.
29 : 87 = 1 : 3

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

1 p = 3 u
3 p = 9 u

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

9 u + 45 = 1 u + 1901
9 u - 1 u = 1901 - 45
8 u = 1856

1 u = 1856 ÷ 8 = 232

Allowance that Brandon received
= 1 u + 1901
= 232 + 1901
= $2133

(b)
Allowance that Albert received
= 3 u
= 3 x 232
= $696

Answers: (a) $2133; (b) $696