Sales Tax and Discount Problem #1 [Algebra]

Sales Tax and Discount Problem #1:

Gina paid $131 for a car stereo on sale for 30% off. There was also a 7% sales tax on the purchase. Find the original price of the stereo.


For the sales tax and discount problem #1:

The original price is missing and the new price after the sales tax and discount is given.

The new price is $131.

30% when converted to decimal is 0.30 while 7% is converted as 0.07.

To get the new price, the 30% discount was deducted, but the sales tax is added based on the discounted price.

Let x be the original price.

0.3x is the discount given that it is 30% of the original price.

Therefore, $$x-0.3x$$ is the discounted price.

The sales tax of the discounted price is: $$0.07(x – 0.3x)$$ provided that it is 7% of the discounted price.

Therefore, 131 = discounted price + sales tax

$$131 = x – 0.3x + 0.07(x – 0.3x)$$

$$131 = x – 0.3x + 0.07(0.97x)$$

Combining like terms:

$$131 = 0.749x$$

$$x = 174.90$$

So, the original price of the car stereo is $174.90.

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