A print shop charges \9 for each color poster. Sam paid a total of \mn$ color posters, which can be represented by the equation If Sam ordered 5 color posters, how many black-and-white posters did he print?

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SAT Linear Equations in Two Variables Question 124 | Free SAT Prep | Aniko

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Question 124·Easy·Linear Equations in Two Variables

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A print shop charges $6 for each black-and-white poster and $9 for each color poster. Sam paid a total of $87 for printing $m$ black-and-white posters and $n$ color posters, which can be represented by the equation

6m + 9n = 87

If Sam ordered 5 color posters, how many black-and-white posters did he print?

For word problems that give a linear equation with two variables and then specify one of the variables, quickly substitute the known value into the equation to reduce it to a one-variable equation. Then use basic algebra: combine like terms, move constants to the other side, and divide to solve for the remaining variable. Always do a fast check by plugging your solution back into the original cost expression to make sure it matches the total given in the problem.

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Use the given number of color posters

You are told Sam ordered 5 color posters. How can you use this to replace $n$ in the equation $6m + 9n = 87$ ?

Simplify after substituting

After you plug in $n = 5$ , multiply $9$ by $5$ and then combine like terms so that the equation has only one variable, $m$ .

Isolate $m$

Once you have an equation of the form $6m + \,\text{(number)} = 87$ , move the number to the other side and then divide by 6 to solve for $m$ .

Desmos Guide

Use Desmos to solve for $m$

In Desmos, type the expression (87 - 9*5)/6 into a new line. The value that Desmos returns for this expression is the solution for $m$ , the number of black-and-white posters.

Step-by-step Explanation

Substitute the number of color posters

We are told Sam ordered 5 color posters, so $n = 5$ .

Substitute $n = 5$ into the equation

6m + 9n = 87

to get

6m + 9(5) = 87.

Simplify and isolate the term with $m$

First compute $9(5)$ :

9(5) = 45.

So the equation becomes

6m + 45 = 87.

Subtract 45 from both sides to isolate the $6m$ term:

6m = 87 - 45.

Now simplify the right side:

6m = 42.

Solve for $m$ and answer the question

To solve for $m$ , divide both sides of $6m = 42$ by 6:

m = \frac{42}{6} = 7.

So Sam printed $7$ black-and-white posters, which corresponds to choice C.

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Step-by-step Explanation

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Step-by-step Explanation