SOLUTION: Dominique is purchasing a car priced at $20,000. At the time of purchase, he will also buy additional equipment for the car, which is priced at d dollars. There is a 5 percent sale

Question 1195403: Dominique is purchasing a car priced at $20,000. At the time of purchase, he will also buy additional equipment for the car, which is priced at d dollars. There is a 5 percent sales tax on Dominique’s total purchase. If he pays $25,200, including tax, for the car and the additional equipment, what is the value of d?

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

The car is $20,000 before tax and any add-ons.
Dominique pays an additional d dollars, where d is some positive real number, for extra equipment.

The pre-tax subtotal is 20,000+d

The after-tax amount is 5% larger, so we multiply by 1.05
Think of it like saying 100% + 5% = 1 + 0.05 = 1.05

So 1.05*(20,000+d) represents the final amount paid when tax is included.
This amount is stated as $25,200

Let's solve for d.
There are at least two ways to do so.

Method 1
1.05*(20,000+d) = 25,200
20,000+d = (25,200)/(1.05)
20,000+d = 24,000
d = 24,000-20,000
d = 4,000

Method 2
1.05*(20,000+d) = 25,200
1.05*20,000+1.05*d = 25,200
21,000+1.05*d = 25,200
1.05*d = 25,200-21,000
1.05*d = 4,200
d = (4,200)/(1.05)
d = 4,000

Feel free to pick your favorite method, or use some other method entirely.

In method 1, I divided both sides by 1.05 and subtracted 20,000 from both sides.
In method 2, I distributed first. Then subtracted 21,000 from both sides. The last step was dividing both sides by 1.05

Answer: $4,000

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