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Eddie has saved up [tex]$\$[/tex]45[tex]$ to purchase a new camera from the local store. The sales tax in his county is $[/tex]7\%[tex]$ of the sticker price. Write an equation and solve it to determine the value of the highest-priced camera Eddie can purchase with his $[/tex]\[tex]$45$[/tex], including the sales tax. Round your answer to the nearest penny.

[tex]\[
\begin{array}{l}
x + 0.07x = 45 \\
1.07x = 45 \\
x = \frac{45}{1.07} \\
x \approx \$42.06
\end{array}
\][/tex]

The highest-priced camera Eddie can purchase, including sales tax, is approximately [tex]$\$[/tex]42.06$.

Sagot :

GinnyAnswer
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.
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