We are asked to determine the percentage of discount if the price for an item goes from $150 to $112.50. To do that we will use the following relationship:
[tex]150-\frac{150x}{100}=112.5[/tex]Where "x" is the percentage of the discount.
Now we solve for "x" first by subtracting 150 from both sides:
[tex]-\frac{150x}{100}=112.5-150[/tex]Solving the operations:
[tex]-\frac{150x}{100}=-37.5[/tex]Now we multiply both sides by 100:
[tex]\begin{gathered} -150x=-37.5\times100 \\ -150x=-3750 \end{gathered}[/tex]Now we divide both sides by -150:
[tex]x=-\frac{3750}{-150}[/tex]Solving the operations:
[tex]x=25[/tex]Therefore, the percentage of the discount is 25%.
