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?

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

part 1 answer = 8

part 2 answer = 72

step-by-step explanation:

part 1 explanation = add all of the numbers, then divide by how many numbers you have. so, 200/25 = 8.

part 2 explanation = not gonna lie, this is hard to explain, so just google how to do it.

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .