Sure, let's solve the problem step-by-step.
Problem: Eddie has saved up [tex]$45 to purchase a new camera. The sales tax in his county is 7% of the sticker price. We need to determine the value of the sticker price of the camera that Eddie can purchase with his $[/tex]45, including the sales tax.
Step 1: Set up the equation
Let [tex]\( x \)[/tex] represent the sticker price of the camera. The sales tax is 7% of the sticker price, so the total amount payable including the sales tax is given by:
[tex]\[ x + 0.07x = 45 \][/tex]
Step 2: Simplify the equation
Combine like terms:
[tex]\[ 1.07x = 45 \][/tex]
Step 3: Solve for [tex]\( x \)[/tex]
To solve for [tex]\( x \)[/tex], divide both sides of the equation by 1.07:
[tex]\[ x = \frac{45}{1.07} \][/tex]
Step 4: Calculate the sticker price
[tex]\[ x = \frac{45}{1.07} \approx 42.05607476635514 \][/tex]
Step 5: Round to the nearest penny
Round the sticker price to the nearest penny:
[tex]\[ x \approx 42.06 \][/tex]
So, the value of the sticker price of the camera that Eddie can purchase with his [tex]$45, including the sales tax, is approximately $[/tex]42.06.
