Caden's and Cathy's monthly allowances were the same at first. Caden's allowance increased by 45% while Cathy's decreased by 35%. Given that Caden's allowance would decrease by another 20% if he had received $812 less from his mothers, find the difference in the children's monthly allowances.

	Caden	Cathy
Before	1 u	1 u
Change 1	+ 0.45 u	- 0.35 u
After 1	1.45 u	0.65 u
Change 2	- 0.29 u	No change
After 2	1.16 u	0.65 u

Increase in Caden's allowance
= 45% x 1 u
= ⁴⁵₁₀₀ x 1 u
= 0.45 u

Decrease in Cathy's allowance
= 35% x 1 u
= ³⁵₁₀₀ x 1 u
= 0.35 u

Decrease in Caden's allowance if he had received $812 less from his mothers
= 20% x 1.45 u
= ²⁰₁₀₀ x 1.45 u
= 0.29 u

0.29 u = 812

1 u = 812 ÷ 0.29 = 2800

Difference in the allowance between Caden and Cathy
= 1.45 u - 0.65 u
= 0.8 u
= 0.8 x 2800
= $2240

Answer(s): $2240