# Writing Equations

## Algebra: Writing Equations

Read the following SAT test question and then select the correct answer.

Read the question carefully so that you don’t miss any important information.  Identify the bottom line and assess your options to find it.  Choose the most efficient method to attack the problem.  Always loop back to make sure that your answer addresses the bottom line.

Milk costs x cents per half-gallon and y cents per gallon. If a gallon of milk costs z cents less than 2 half-gallons, which of the following equations must be true?

Bottom Line: equation

Assess your Options:  The question asks you about "the following equations," so your first instinct is going to be to look down at the answer choices.  Don’t do it!  Most of them are wrong and they are there to distract you from the correct answer.  Instead, write your own equation using what you know from the problem.

Attack the Problem: Start with what you know: “Milk costs x cents per half-gallon and y cents per gallon.”  Make a note:

x = half-gallon
y = gallon

Now look at the conditions that you are given “a gallon of milk costs z cents less than 2 half-gallons.”  The word “costs” is just like the word “is;” it shows you where to put the equal sign.  The words “less than” signal that you will need to subtract the z. Use the variables you have been given to write an equation.

y = 2x – z

Once you have an equation, glance down at your answer choices.  Notice that all of them are set equal to zero, and all the x values are positive.  Set your equation equal to zero and keep the x value positive by subtracting the y variable from each side.

0 = 2xz – y

As you look at your answer choices, realize that when you are adding and subtracting numbers, order does not matter.  In fact, all of the answers have the variables arranged alphabetically.  Do the same to your equation.

0 = 2x – y – z

Loop Back:  You can be confident in your answer because you reached it by writing your own equation.

(A) x – 2y + z = 0
(B) 2xy + z = 0
(C) x – y – z = 0
(D) 2x – y – z = 0
(E) x + 2y – z = 0

The correct answer is (D).

On sat.collegeboard.org, 56% of the responses were correct.

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