A grocery store bought milk for $2.60 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 15 half gallons. If the remaining milk is sold for $4.08 per half gallon, how many half gallons did the store buy if they made a profit of $69.04?

88 half gallons

Step-by-step explanation:

We can solve this problem by creating an equation. First we will need a variable. Since we are trying to find how many half gallons the store bought, that will be what our variable represents.

Let g = the number of half gallons

Since the store bought milk for $2.60 per half gallon, the amount of money they spent will be 2.6g.

The remaining milk is sold for $4.08 per half gallon. Remember, the store lost 15 half gallons so the number of gallons is currently g-15. This means that to find the amount of profit they made, we use 4.08(g-15).

We already know that the profit is $69.04, so we can make this into an equation.

This profit is the amount of money made minus the cost.

4.08(g-15) - 2.6g = 69.04

We can begin to solve this by simplifying the left side.

4.08(g-15) - 2.6g

4.08g - 61.2 - 2.6g

1.48g - 61.2

This makes our new equation:

1.48g - 61.2 = 69.04

We can begin to isolate our variable, g, by adding 61.2 to both sides.

1.48g = 130.24

Then we divide both sides by 1.48.

g = 88

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204