Question

The sales tax on a new car varies directly to (or is directly proportional to) the price of the car. If $1,800 in sales tax is paid for a $25,000 car, what is the purchase price of a car worth $1,600 in sales tax?

Answer 1

You know that you pay $1800 on a $25000 car. What you need to know is the value of a car when you spend $1600 in tax. You can do this by cross-multiplying:

\[\frac{1800}{25000} = \frac{1600}{x}\]

Answer 2

okay

Answer 3

So 1,800x=4,000,000

Answer 4

And x = 2,222.22 Thank you!

Answer 5

Close, but it's not 4 million.

Answer 6

It's 40 million.

Answer 7

But your technique is right. Good job.

Answer 8

Thanks

Answer 9

No problem. And it makes sense that the car in \(x\) should be about the same cost as the first car, since the taxes paid are about the same, too.

Answer 10

So its actually $22,222.22

Answer 11

And the same thing goes for this problem right? The time it takes to complete a project varies inversely (or is inversely proportional to) the number of people working on the project. If a project takes 6 hours to complete with 2 people, how many people are needed to complete the same project in 3 hours?

Answer 12

Yes, it's the same idea.

Answer 13

Okay thanks