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:
[tex]105\%=1.05[/tex]
So, the value of x after the sales tax will be:
[tex]x\cdot1.05[/tex]
Since she has 80, this final price can be at most 80, so:
[tex]80=x\cdot1.05[/tex]
Now, we just need to solve it.
To do it, let's first switch the sides so the variable x is to the left:
[tex]\begin{gathered} 80=x\cdot1.05 \\ x\cdot1.05=80 \end{gathered}[/tex]
Now, we can divide both sides by 1.05 so that we nd up with only x on the left side:
[tex]\begin{gathered} x\cdot1.05=80 \\ \frac{x\cdot1.05}{1.05}=\frac{80}{1.05} \\ x=76.19047\ldots \\ x\approx76.19 \end{gathered}[/tex]
So, she can spend approximately $76.19 on items.
