Algebra 1 Word Question

Question

The cost to manufacture x units of a certain product is given by C(x)=x²-60x+2700. Find the number of units that can be manufactured for a cost of $6700

Answer 1

c(x) = 6700

6700 = x^2 - 60x + 2700

x^2 - 60x + 2700 = 6700

x^2 - 60x - 4000 = 0

(x-100)(x+40) = 0

x = 100 or x = -40 (not valid)

number of units = 100

Answer 2

The cost to manufacture x units of a certain product is given by C(x)=x²-60x+2700. Find the number of units that can be manufactured for a cost of $6700

Given total cost = 6700

x = Number of units

So 6700 = X² -60X +2700

subtracting 6700 from both sides

6700 -6700 = X² -60X [phone]

0 = X² - 60X - 4000

We need to solve this equation for X

Rewriting this equation

X² - 60X -4000 = 0

Solving for X

X = 30 + √1300 and X = 30 - √1300

So x values are 30 + 36.05 or -36.05

So the Answer is 66 units