1) An exam will have 20 questions worth a total of 100 points. There will be True-False questions worth 3 points each and short essay questions worth 11 points each. Several students ask how many essay questions there will be, but the teacher won't tell. How many essay questions will there be.

let x = number of true-false questions

let y = number of essay questions

x + y = 20
3x + 11 y = 100

Solve those two equations. I assume you know how. Substitution is one way.

I got 15 T-F Questions

and 5 Essay Questions.

is that right ??

check: 45 + 55 = 100

Looks good!

Thank You very mcuh.

:]

To find out how many essay questions there will be, we need to consider the total number of questions worth 100 points and the points assigned to each type of question.

Let's assume there are x essay questions and (20 - x) True-False questions (since there are a total of 20 questions).

Since each essay question is worth 11 points, the total points earned from the essay questions would be 11 * x.

Since each True-False question is worth 3 points, the total points earned from the True-False questions would be 3 * (20 - x).

To find the total number of points, we can equate the points earned from essay questions and the points earned from True-False questions to 100:

11x + 3(20 - x) = 100

Simplifying the equation:
11x + 60 - 3x = 100
8x = 40
x = 5

Therefore, there will be 5 essay questions.