Question

let x = boxes of candles, and each box holds 12 candles. 1. mark knows that the fixed cost is $500 and the total cost to produce 100 boxes is $1,500. help the children determine the cost function c(x), given that it is linear.

Explanation:

Step1: Recall linear cost function form

A linear cost function is $C(x) = mx + b$, where $b$ is fixed cost, $m$ is variable cost per unit, and $x$ is number of units.

Step2: Identify given values

Fixed cost $b = 500$. When $x=100$, $C(100)=1500$.

Step3: Solve for variable cost $m$

Substitute into the function:
$1500 = 100m + 500$
Subtract 500 from both sides:
$1500 - 500 = 100m$
$1000 = 100m$
Divide both sides by 100:
$m = \frac{1000}{100} = 10$

Step4: Write the cost function

Substitute $m=10$ and $b=500$ into $C(x)=mx+b$.

Answer:

$C(x) = 10x + 500$