A printing company uses the function to determine the total cost , in dollars, of producing custom coffee mugs. If the total cost is \$300, how many mugs are produced?

Solution available with step-by-step explanation

SAT Linear Functions Question 52 | Free SAT Prep | Aniko

00:00

Question 52·Easy·Linear Functions

0 / 140

A printing company uses the function

c(x)=12x+60

to determine the total cost $c(x)$ , in dollars, of producing $x$ custom coffee mugs. If the total cost is $300, how many mugs are produced?

For linear cost function problems, immediately plug the given total cost into the function, set up an equation, and solve step by step: first undo any added or subtracted constant (fixed cost), then undo the multiplication (per-item cost). Keep track of what the variable represents so you can interpret your final value in context and check that it is reasonable (for example, it should be a positive, whole number of items).

Hints

Click me!

Use the cost function with the given total cost

You are told the total cost is $300. How can you use this information with the function $c(x) = 12x + 60$ ?

Set up an equation to solve for $x$

Replace $c(x)$ in the function with $300$ and write an equation with $x$ as the only variable. What equation do you get?

Isolate $x$ step by step

Once you have your equation, first undo the $+60$ , then deal with the $12$ multiplied by $x$ . What operations should you use, in what order?

Remember what $x$ represents

After you solve for $x$ , think about what $x$ stands for in the context of the problem (number of mugs).

Desmos Guide

Enter the cost function

In Desmos, type y = 12x + 60 to graph the cost function.

Represent the $300 cost

On a new line, type y = 300 to graph a horizontal line showing a total cost of $300.

Find the number of mugs

Look for the intersection point of the two graphs. The x-coordinate of this intersection is the number of mugs produced when the cost is $300.

Step-by-step Explanation

Write the equation for this specific situation

You are told the total cost is $300, and the cost function is

c(x) = 12x + 60.

So set $c(x)$ equal to $300$ :

300 = 12x + 60.

Now you just need to solve this equation for $x$ .

Isolate the term with $x$

To get $x$ by itself, first remove the constant term $60$ from the right side.

Subtract $60$ from both sides:

300 - 60 = 12x + 60 - 60

240 = 12x.

Now the equation is simpler: $12x = 240$ .

Solve for $x$ and interpret the result

Now divide both sides of $12x = 240$ by $12$ to solve for $x$ :

\frac{12x}{12} = \frac{240}{12}

x = 20.

Since $x$ is the number of mugs, the company produces 20 mugs when the total cost is $300.

Strategy

Hints

Desmos Guide

Step-by-step Explanation

Study Hints

Strategy

Hints

Desmos Guide

Step-by-step Explanation