Question

Solve by simplifying the problem. There are 18 students in Mr. Alvarez’s art class. Throughout the year, every student must pair up with every other student to complete a project. How many projects will be finished?
A. 149 projects
B. 153 projects
C. 171 projects
D. 135 projects

Answer 1

There are 18 students in the classroom. From the 18 students, one of them will be doing a project with each one of them. \[18*(18-1) = 18 * 17 = 306\]however if we go with that number we will have a wrong answer because we have actually checked the problem twice.

Explanation:
Say a student A and B are doing a project together. We have calculated this in the formula above, but we have also calculated the fact that B and A are doing the project. So we have two same results instead of one. Therefore to correct for this we must divide by two.

Result:
\[\frac{ 18-17 }{ 2 } = \frac{ 306 }{ 2 } = 153\]Hence your answer is B.

Answer 2

Thank you!