The life expectancy of a circulating coin is 20 years. the life expectancy of a circulating dollar bill is only startfraction 1 over 20 endfraction as long. find the life expectancy of circulating paper money.

One year because 20 years is 20/20=1 10 years is 10/20=1/2 and five years is 5/20=1/4 etc.

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