To obtain a rough estimate of the development cost, Abigail, the accountant working for Pinecrest Enterprises, assumes that the total cost C (in millions of dollars) is given by the formula C= 20y + 15, where y is the cost per subdivision. If x represents the cost of a single family home in a subdivision, then the cost per subdivision y is given by the formula y= 50 x + 5.
Find the formula for the total cost C as a function of x. Enter your answer in the form C = mx+b.
y(x) = 50x+5
C(y) = 20y+15
So,
C(x) = 20(50x+5)+15 = 1000x+115
To find the formula for the total cost C as a function of x, we need to substitute the formula for y into the equation for C.
Given: y = 50x + 5
Substituting this into the equation for C:
C = 20y + 15
C = 20(50x + 5) + 15
C = 1000x + 100 + 15
C = 1000x + 115
Therefore, the formula for the total cost C as a function of x is C = 1000x + 115.