Answer: her monthly allowance is $630
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