One group of parents is determined to sell sugar cookies. They are having a hard time
understanding that not all of the money made from the sale of cookies will be profit,
because it costs money to purchase the ingredients to make the cookies. You have
determined the cost to make each cookie (x) is this:
c= 100
_____
4x-28
1a. What would it cost for ingredients , per cookie, to make 100 cookies?
c=
100
100
100
100
=
=
=
= $0.27 per cookie
4x − 28 4 (100 ) − 28 400 − 28 372
1b. What would it cost for ingredients , per cookie, to make 500 cookies?
c=
100
100
100
100
=
=
=
= $0.05 per cookie
4x − 28 4 ( 500 ) − 28 2000 − 28 1972
1c. The committee decides to sell the cookies for $0.50 each. What would the profit be,
per cookie, if 200 cookies were made and sold?
c=
100
100
100
100
=
=
=
= $0.13 per cookie
4x − 28 4 ( 200 ) − 28 800 − 28 772
Profit = $0.50 - $0.13 = $0.37 per cookie
1d. If the cookies sell for $0.50 each, what would the profit be, per cookie, if 600 were
made and sold?
c=
100
100
100
100
=
=
=
= $0.04 per cookie
4x − 28 4 ( 600 ) − 28 2400 − 28 2372
Profit = $0.50 - $0.04 = $0.46 per cookie
1e. When determining how many cookies to bake, would you advise the parents to make
more cookies or fewer cookies based on what you found in 1a, b, c and d? Why?
The parents should be advised to bake more cookies because the average cost
of the ingredients is decreased when more cookies are made. The profit per cookie
sold is increased when the cost of the ingredients is decreased.
1f. How many cookies would make the equation for cost undefined?
The cost equation will be undefined when the denominator is equal to zero.
Setting the denominator equal to zero and solving for x gives:
4x – 28 = 0
4x = 28
4x / 4 = 28 / 4
x=7
The cost equation is undefined when the number of cookies equals 7.
2a. Another group of parents is going to sell specialty coffee drinks including espresso,
lattes, cappuccinos and mochas. It cost $250 to rent the equipment, which is a fixed cost.
Additionally, the ingredients for each drink (x) cost $0.25. Write an equation that shows
the total cost to make specialty coffee drinks.
c ( x ) = 250 + 0.25x
2b. The average cost per drink can be found by dividing the total cost (what you found in
2a) by the number of drinks sold (x). Write an equation that shows the average cost per
drink.
c ( x) =
250 + 0.25x
x
2c. If 100 specialty coffee drinks were sold at the bake sale, what would the average cost
per drink be?
c (100 ) =
250 + 0.25 (100 ) 250 + 25 275
=
=
= $2.75
100
100
100
2d. If 250 specialty coffee drinks were sold at the bake sale, what would the average cost
per drink be?
c ( 250 ) =
250 + 0.25 ( 250 ) 250 + 62.5 312.5
=
=
= $1.25
250
250
250
2e. If 500 specialty coffee drinks were sold at the bake sale, what would the average cost
per drink be?
c ( 500 ) =
250 + 0.25 ( 500 ) 250 +125 375
=
=
= $0.75
500
500
500
2f. What happens to the cost as you sell more drinks? Would the cost to make each drink
ever go below $0.25?
The average cost of the drinks decreases as you sell more drinks.
No, the average cost cannot ever go below $0.25, since that is the cost of each
additional drink.
3a. The average cost for ingredients per cookie was given to you for problem 1. For
problem 2, you found the average cost per drink in 2b. The committee wants to know, if
you sell the cookie and the drink together, what the equation would be that represents the
average cost for the pair.
c ( cookie and drink ) =
250 + 0.25 ( x )
100
+
4x − 28
x
3b. If they sold 100, what would the cost be for ingredients per set?
c (100 cookies and drinks) =
=
250 + 0.25 (100 )
100
+
4 (100 ) − 28
100
100 275
+
372 100
= 0.27 + 2.75
= $3.02