*** Katherine went to Hibbet sports and spent $125.50 on a pair of shoes and $12.25
on a t-shirt. If the sales tax is 8.25%, how much will she pay in all?

How much was the tax?

125.50 + 12.25 = 137.75

137.75/109 X 108.25 = 149.114375

total cost = $149.11

149.11 - 137.75= 11.36

sales tax = $11.36

the answer is 5636.7

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4