Question

1. karla paid $29.16 for a sweater, which includes a tax of 8%. what was the price of the sweater before tax?
2. a video game is on sale for 15% off. the sale price of the game is $55.25. what was the original price?

Explanation:

Question 5

Step1: Define the variable

Let \( x \) be the price of the sweater before tax. The tax is 8% of \( x \), so the total price paid is the original price plus the tax, which can be written as \( x + 0.08x \).

Step2: Set up the equation

We know the total price paid is $29.16, so the equation is \( x + 0.08x = 29.16 \). Combining like terms, we get \( 1.08x = 29.16 \).

Step3: Solve for \( x \)

To find \( x \), we divide both sides of the equation by 1.08: \( x=\frac{29.16}{1.08} \). Calculating the right - hand side, \( \frac{29.16}{1.08}=27 \).

Step1: Define the variable

Let \( y \) be the original price of the video game. The video game is on sale for 15% off, so the sale price is the original price minus 15% of the original price. Mathematically, the sale price is \( y-0.15y = 0.85y \).

Step2: Set up the equation

We know the sale price is $55.25, so the equation is \( 0.85y=55.25 \).

Step3: Solve for \( y \)

To find \( y \), we divide both sides of the equation by 0.85: \( y = \frac{55.25}{0.85} \). Calculating the right - hand side, \( \frac{55.25}{0.85}=65 \).

Answer:

The price of the sweater before tax was $27.

Question 6