D) = 7. Choose it!Inequalities
Plugging In works on problems containing inequalities, but you will have to follow some different rules.
Plugging in one number is often not enough; let’s look at an example where this is the case.
6.Mammoth Printing Company charges a fee of $28 to print an oversized poster, and $7 for
each color of ink used in the poster. Colossal Printing charges a fee of $34 to print an
oversized poster and $5.50 for each color of ink used. If x represents the number of colors
of ink used to print a poster, what are all the values of x for which Mammoth Printing
Company would charge more to print the poster than Colossal Printing?
A) x < 4
B) 2 ≤ x ≤ 4
C) 4 ≤ x ≤ 7
D) x > 4Here’s How to Crack It
Since you are looking for an amount that would make the Mammoth Printing Company’s price greater
than Colossal Printing’s price, you have an inequality.
Plugging In on an inequality question means selecting a value for x that answers the question, and then
comparing it to the inequalities in the answer choices. Remember, you may have to try more than one
number with inequality questions, since the number you try first may satisfy the inequality in more than
one answer choice!
Let’s start out by trying something small, like x = 2. Since x is the number of colors of ink used, Mammoth
Printing Company would charge $28 to print the poster, plus $7 for each of the 2 colors, for a total of $42.
Colossal Printing would charge $34 to print the poster, plus $5.50 for each of the 2 colors, or $45 total.
That means that when x = 2, Mammoth Printing Company would charge less than Colossal Printing, and 2
is not a number that works as a solution to this problem.
Let’s try something bigger, say x = 5. If the poster had 5 colors, Mammoth Printing Company would
charge $28 to print the poster, plus $7 for each of the 5 colors, for a total of $63. Colossal Printing would
charge $34 to print the poster, plus $5.50 for each of the 5 colors, or $61.50 total. That means that when x
= 5, the price Mammoth charges would be more than Colossal’s price, so this is a possible value for x.
Once you have a value for x that satisfies the question, it’s time to move to the answer choices. You
should eliminate (A) and (B), because x = 5 does not satisfy either of those inequalities. Choices (C) and
(D) are satisfied when x = 5, so they are still possible.