The manager of the ice cream shop noticed that 90% of all club members brought along a family member who spent an average of $18 in the shop. The tax on their bill was 5.5%. What was the total amount spent by the family members in one year?

180

step-by-step explanation:

the answer to this question is 3/19

step-by-step explanation:

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