## Algebra: Equations

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

*If a, b, and c are numbers such that and , then is equal to which of the following?*

**Bottom line**:

**Assess your Options**: There are two ways that you can solve this equation, and both will arrive at the correct answer. You can solve it algebraically by substituting information into the equation, or you can pick your own numbers for the variables. Choose the method that is easier and faster for you.

**Attack the problem**: If you are going to solve a problem algebraically, always look for ways to simplify the problem that you are given. In this case, you will want to get rid of unnecessary fractions. Look at the first piece of information that you are given. If

*a*divided by

*b*is 3, you can get rid of the fraction by multiplying each side of the equation by

*b*.

*a*= 3

*b*.

*b*for

*a*. Now you have 3

*b*+

*b*, which will simplify to 4

*b*.

*b*+

*c*? You might be tempted to substitute 7

*c*for

*b*, but remember your goal is to get to a number without a variable. If you have the same variable in the top and bottom, the two variables cancel. Therefore, you need to find what

*c*is equal to in terms of

*b*.

*b*divided by

*c*is 7, then you know that c divided by b is 1 over 7. You flip both equations. Solve for

*c*by multiplying both sides of the equation by

*b*.

*b*moves to the bottom of the second fraction and cancels out. You solved the equation!

**Alternatively:**If you dislike algebra, use the strategy of picking numbers to solve this problem. You want to get rid of ugly fractions, and the best way to do that is to put a number over 1. You cannot just put

*b*= 1 because

*b*affects two different equations and you might end up with numbers that are difficult to use in your other equation. However,

*c*is on the bottom of a fraction in one equation. Pick

*c*= 1. Plug 1 into the second piece of information with

*c*and solve for

*b*.

*b*= 7.

*b*must equal 7. Now plug that into the first piece of information that you were given. If

*b*is 7, then

*a*must equal 21.

*a*= 21.

*a*,

*b*, and

*c*, plug those into your bottom line equation:

**Bottom Line:**As soon as you have a value to represent your bottom line, look down at your answer choices.