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22 May, 22:55

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?

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  1. 22 May, 23:25
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    Rita paid 47,500 dollars for the purchase price.

    Step-by-step 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
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