To make 1 1/2 dozen muffins, a recipe uses 3 1/2 cups of flour. How many cups of flour are needed for every dozen muffins made?​

Step-by-step explanation:

n = # cup(s) of flour

1.5 muffins            x       12 (dozen muffins)       > fractions

3.5 cups of flour            n

12 x 3.5 = 1.5 (n)

42 = 1.5 (n)   > multiply 12 and 3.5

42/1.5 = n   > divide 1.5 on both sides, cancels out on right

28 = n # cups of flour

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