An exam worth 269 points contains 36 questions. some questions are worth 7 points, and the others are worth 8 points. how many 7 point and 8 point questions are on the test?

There are 19 questions worth 7 points.

There are 17 questions worth 8 points.

Step-by-step 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.