Write the ratio of 42 coins/98 bills as a fraction in the simplest form

3 coins / 7 bills

Step-by-step explanation:

42c/98b --(:2)--> 21c/49b --(:7)--> 3c/7b

OR

42c/98b ---( : 14 = (2*7))--> 3c/7b

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