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Emma can spend $____ on items.(Round to the nearest cent as needed.)

Emma can spend $____ on items.(Round to the nearest cent as needed.)-example-1

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To calculate the total price after applying the sales tax, we just need to apply the sales tax to the final values of the items.

Let x be how much she can spent on items.

To apply 5% in x, this means we want to calculate the total value plus 5%, that is, 105%.

So, we can multiply x by 105%.

However, we need to do this with the percentage in the decimal form:


105\%=1.05

So, the value of x after the sales tax will be:


x\cdot1.05

Since she has 80, this final price can be at most 80, so:


80=x\cdot1.05

Now, we just need to solve it.

To do it, let's first switch the sides so the variable x is to the left:


\begin{gathered} 80=x\cdot1.05 \\ x\cdot1.05=80 \end{gathered}

Now, we can divide both sides by 1.05 so that we nd up with only x on the left side:


\begin{gathered} x\cdot1.05=80 \\ (x\cdot1.05)/(1.05)=(80)/(1.05) \\ x=76.19047\ldots \\ x\approx76.19 \end{gathered}

So, she can spend approximately $76.19 on items.