Last year a pair of shoes cost $35. this year the price of the shoes has increased to 115% of the original price. what is the new price of the shoes?

When a problem says that the price was increased by 100% + n%, it means you add on n% percent of the original price. In this problem, the original price was $35. The new price is 115% percent of the original price. So all we need to do is find 15% of the original price and add it onto the original price to find the new price.
$35 * 0.15 = $5.25
$35 + $5.25 = $40.25
The new price of the shoes is $40.25.

115% = 1.15

1 + 1.15 = 2.15

$35 * 2.15 = $75.25

new price of the shoes = $75.25