Question

Please Help!

Juanita Wade's new car has an MSRP of $28,902.11 including title and processing fees. The Premier Package which includes surround sound and DVD player costs three times the amount of the In-Style Package which includes leather seats and select wheels. The total cost of her new car was $34,290.08 which included the 6.5% sales tax. Find the cost of the Premier Package to the nearest cent.


(This is a fill in the blank question. Thank you!)

Answer 1

`\boxed{\$3295.15}\\`

Explanation:

Step 1. Calculate the extra cost

`\begin{array}{rcr}\text{MSRP + Package + tax} & = & \$34 290.08\\\text{-MSRP} & = & -28 902.11\\\text{Package + tax } & = & \$5387.97\\\end{array}`

Step 2. Calculate the sales tax

Package + tax = $5387.97

MRSP + package + tax = total cost

For simplicity, let

m = MSRP

p = package

t = tax

c = total cost

m + p + t = c

Tax = 6.5% of (MSP + package)

t = 0.065(m+ p)

m + t + 0.065m + 0.065p = c

`\begin{array}{rcr}1.065m +1. 065p & = & 34 290.08\\1.065 * 28 902.11 + 1.065p & = & 34 290.08\\30780.75 + 1.065p & = & 34290.08\\1.065p & = & 3509.33\\\end{array}\\`

`p = (3509.33 )/(1.065 )\\`

`\boxed{=\$3295.15}\\`

Check:

`\begin{array}{rcr}\\\text{MSRP } & = & \$28 902.11\\\text{+ Package } & = & +3295.15\\\text{Cost } & = & 32 197.26\\\text{+ 6.5 \% tax } & = & +2092.82\\\text{Cost + tax } & = & \$34 290.08\\\end{array}\\`