Question

The amount of sales tax on a new car is directly proportional to the purchase price of the car. Victor bought a new car for $30,000 and paid $1,500 in sales tax. Rita bought a new car from the same dealer and paid $2,375 sales tax. How much did Rita pay for her car?

Answer 1

Rita paid 47,500 dollars for the purchase price.

Explanation:

We are given the sales tax on a new car is directly proportional to the purchase price of the car which means there is is something k such that

when you multiply it to the sales tax you get the purchase price.

Let's set this equation:

y=kx

Let y represent the purchase price and x the sales tax.

The second sentence tells us that (x,y)=(1500,30000).

We can plug this into y=kx to find the constant k. (Constant means it stays the same no matter what the input and output is).

So we have:

30000=k(1500)

300 =k(15) I went ahead and divided previous equation by 100.

Now divide both sides by 15:

300/15=k

Simplify:

20=k

So the equation to use the answer the question is

y=20x

where y is purchase price and x is sales tax.

So we want to know the purchase price on a car if the sales tax is 2375.

So replace x with 2375:

y=20(2375)

y=47500

Answer 2

$47500

Explanation:

If the amount of sales tax on a new car is directly proportional to the purchase price of the car and Victor bought a new car for $30,000 and paid $1,500 in sales tax and Rita bought a new car from the same dealer and paid $2,375 sales tax, Rita payed $47,500 for her car.

y=20(2375)

y=47500