Writing Equations

Algebra: Writing Equations

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

Use the same method for all SAT math questions.  Read the question carefully, identify the bottom line, assess your options for reaching the bottom line, and choose the most efficient option to attack the problem.  When you have an answer, loop back to make sure that it matches your bottom line.

A geologist has 10 rocks of equal weight. If 6 rocks and a 10-ounce weight balance on a scale with 4 rocks and a 22-ounce weight, what is the weight, in ounces, of one of these rocks?

Bottom line: Remember to write your bottom line in easy-to-understand shorthand. You could write "weight of 1 rock = ?" but "w = ?" is much shorter. 

Assess your options: You could try each of your answer choices in this scenario, but that will waste time because you will most likely need to try multiple answers.  Start by writing an equation so that you only have to solve one problem.

Attack the problem:  On one side of the scale you have 6 rocks and a 10 oz. weight.  You don’t know how much each rock weighs, so you will need to add a variable to represent that number.  There are 6 of that missing weight (w), plus 10 oz.

6w + 10

All of this balances with, is equal to, 4 rocks of the same weight plus 22 oz.

6w + 10 = 4w + 22

Now solve the equation that you wrote by combining like terms and isolating the variable.

2w + 10 = 22

2w = 12

w = 6

Loop Back: You solved for the weight of one rock, so you are ready to look down at your answer choices.

(A) 4

(B) 5

(C) 6

(D) 7

(E) 8

The correct answer is (C).

On sat.collegeboard.org, 67% of the responses were correct.

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