Read the following SAT test question and then
select the correct answer.
Always read the question carefully and identify
the bottom line so that you do not waste time finding something unrelated to
the question. Assess your options for
solving the problem and choose the most efficient method to attack the
problem. When you have an answer, take a
second or two to loop back and make sure that your answer matches the bottom
If a, b, and c are numbers such that and ,
then is equal to which of the following?
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.
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.
Now you have a = 3b.
Look at the numerator (the top part of the
fraction) of your bottom line. You can
now make sure that there is only one variable in this portion of the
equation. Substitute 3b for a. Now you have 3b +
b, which will simplify to 4b.
Here are the steps you just completed:
Look at the denominator of your equation. How can you simplify b + c? You might be tempted to substitute 7c 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.
When you are given the information that 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.
Plug this information into your bottom line equation
and combine like terms.
A fraction over a fraction is ugly, but
remember that dividing by a fraction is the same thing as multiplying by the
reciprocal of that fraction. In other
Notice that the variable b moves to the bottom of the second fraction and cancels out. You solved the equation!
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.
The variable 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.
Now that you have numbers
for a, b, and c, plug those into your bottom line equation:
Line: As soon as you have a value to
represent your bottom line, look down at your answer choices.
The correct answer is (A).