Eggs can be packaged 12 (1 dozen) to a carton while English muffins are generally sold in packages of 8. How many of each would you buy to make egg muffin sandwiches (1 egg per muffin) so that you would use the same number of eggs and muffins with no extra eggs or muffins left over. Explain how you solved the problem.

24+x=y

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