You took a test. The test was worth 114 points. There were 30 questions on the test. If questions were worth either 2 or 5 points each, how many 2-point questions were there on the test? How many 5-point questions were on the test?
We can set up we have 2 variables for this problem.
x = # of 5 point questions
y = # of 2 point questions
Since we have 2 variables, we need 2 equations, and we have those equations.
We know that...
\(x + y = 30\)
\(5x + 2y = 114\)
To solve, we first have to make it a one variable equation.
Since \(x = 30 - y\), we can replace all of the \(y\) with \(30 - x\).
So \(5x + 2y = 114\) changes to \(5x + 2(30-x) = 114\)
\(5x + 2(30-x) = 114\)
\(5x + 60 - 2x = 114\)
\(3x + 60 = 114\)
\(3x = 54\)
\(x = 18\)
\(y = 12\)
Your answer is...
There are 18 5 point questions and 12 2 point questions.
And you are done! :)