Claire spent $450 of her allowance each month and saved the rest. If she increased her spending by 18% her savings would decrease by 30%. How much was her monthly allowance?

Answer: her monthly allowance is $630

Step-by-step explanation:

Let x represent her monthly allowance.

Claire spent $450 of her allowance each month and saved the rest. This means that the amount she saved each month is x - 450

If she increased her spending by 18% her savings would decrease by 30%. The expression for an 18% increase in her spending would be

(18/100 * 450) + 450 = 81 + 450

= 531

The expression for a 30% decrease in her savings would be

(x - 45) - [30/100 * (x - 450) ]

= (x - 45) - [0.3 (x - 450) ]

= (x - 45) - [0.3x - 135]

= x - 45 - 0.3x + 135

= x - 0.3x - 45 + 135

= 0.7x + 90

Therefore,

0.7x + 90 = 531

0.7x = 531 - 90

0.7x = 441

x = 441/0.7

x = $630