# Every Week A Grocery Store Buys 30 Gallons Of Milk At A Cost Of \$1.58 Per Gallon. The Owner Anticipates A 15% Spoilage Rate. In Order To Acheive A 20% Markup Based On Selling Price, What Should Be The Selling Price Per Gallon?

Let's define S to be the selling price, R to be the actual revenue achieved.

[eq1] R = S - 15%S    (15% of the product cannot be sold, due to spoilage)
= S(100%-15%)
R = S*.85

[eq2] \$1.58 + 20%R = R    (our markup is 20% of realized sales*)

\$1.58 = R(100%-20%)    (subtract 20%R from both sides of [eq2])
\$1.58/.80 = R    (divide both sides by 80%)

\$1.58/.80 = S*.85    (substitute into [eq1])
\$1.58/(.80*.85) = S    (divide both sides by .85)
\$1.58/.68 = S
\$2.32 = S

The price marked on the milk should be \$2.32 per gallon to achieve the desired markup percentage.
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If you want to achieve a "profit" of 20% of the value of selling all 30 gallons, then the price needs to be somewhat higher. I compute it as \$2.43.
Note, too, that 15% of 30 gallons is 4.5 gallons. Spoilage will not be exactly 15% in a given week, but may average that value over several weeks.

thanked the writer.