Hannah finds some dimes and quarters under the couch cushions. How many coins does she have if she has 7 dimes and 5 quarters? How
many coins does she have if she has d dimes and a quarters?

{3 + i, 3 - i, 3, -1}

step-by-step explanation:

answer: 2530

hope this

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