Sherry bought a sport utility vehicle. She received a discount of 18% off the manufacturer's list price but then had to pay 8% state sales tax. If she paid $17,712 for the car after the discount and tax were applied, how much was the manufacturer's list price?

x = $20,000

the manufacturer's list price is $20,000

Step-by-step explanation:

Let x represent the manufacturer's list price.

And c the amount she finally paid

Given that;

She received a discount of 18% off the manufacturer's list price

= x - 18%x

= x - 0.18x

= 0.82x

then had to pay 8% state sales tax.

C = (0.82x) + 8% of (0.82x)

C = 0.82x + 0.08 (0.82x)

C = 0.82x + 0.0656x

C = 0.8856x

Since she paid $17,712

C = $17,712

C = $17,712 = 0.8856x

0.8856x = $17,712

x = $17,712/0.8856

x = $20,000

the manufacturer's list price is $20,000