Function and profit

Question

Ollie sells lemonade. The profit p, in dollars is a function of the number of cups of lemonade,c, that he sells. The function that represents this relationship is p(c) = 3g-15. If Ollie made a profit of $81, how many glasses did he sell?

Answer 1

Losapina, there is an issue here. If you have a function of c, p(c), the other side should say 3c - 15. 

 

If the right side is going to say 3g - 15, we have a function of g, or p(g). Someone made an error by swapping cups and glasses and c and g.

 

I'm going to use p(c).

 

81 = 3c - 15

96 = 3c

c = 32

 

He sold 32 CUPS of lemonade.

 

Or...

 

81 = 3g - 15

96 = 3g

g = 32

 

He sold 32 GLASSES of lemonade.

 

It may seem silly to differentiate, but it's about like saying, "John uses 6 tomatoes per jar of spaghetti sauce. How many teaspoons of oregano does he use for 3 jars of sauce?" Even though glasses and cups can mesn the same thing, we have to use the same variable.