A word problem that I am not grasping

Question

Tanisha bakes cakes and sells them at the school fair. Her initial cost for the fair was $40.00. She figures that each cake costs $2.50 to make, and she charges $6.50 per cake. Let x represent the number of cakes sold.

 

a. Express the cost C as a function of x.

b. Express the revenue R as a function of x.

c. Determine the value of x for which revenue equals cost.

Answer 1

Express the cost C as a function of x or C = f(x)

 

Cost = $2.50x

 

Express the revenue R as a function of x or R = f(x)

 

Revenue = $6.50x

 

Determine the value of x for which revenue equals cost or R = C

 

6.50x = 2.50x

 

6.50x - 2.50x = 0

 

4x = 0; x = 0

 

This makes sense if you simply look at the equations, they are essentially the equations for two lines, with different slopes whose y intercept is zero. Thus, the only place they can share the same value is at the origin or zero. It also makes sense if you look at the logic of the equations themselves; revenue is 2.6 times that of cost, so at no point aside from 0 sales, can they ever be equal