Answer:
There are 19 questions worth 7 points.
There are 17 questions worth 8 points.
Explanation:
Assign variables:
Let x = number of questions worth 7 points.
Let y = number of questions worth 8 points.
First we deal with the number of questions.
There are 36 questions, so our first equation is:
x + y = 36
Now we deal with the points.
x questions worth 7 points each are worth 7x points.
y questions worth 8 points each are worth 8y points.
The total worth of all the questions is 7x + 8y.
The total worth of the exam is 269, so our second equation is
7x + 8y = 269
We have a system of 2 equations in 2 variables.
x + y = 36
7x + 8y = 269
Let's use the substitution method to solve the system of equations.
Solve the first equation for x.
x + y = 36
x = 36 - y
Substitute 36 - y in for x in the second equation.
7x + 8y = 269
7(36 - y) + 8y = 269
Distribute the 7.
252 - 7y + 8y = 269
Combine like terms.
252 + y = 269
Subtract 252 from both sides.
y = 17
There are 17 questions worth 8 points.
x + y = 36
x + 17 = 36
x = 19
There are 19 questions worth 7 points.
Check:
What does 19 questions at 7 points each and 17 questions at 8 points each add to?
19 * 7 + 17 * 8 = 133 + 136 = 269
The points add to 269, so our answer is correct.