The next Algebra test is worth 100 points and contains 35 problems. Multiple-choice questions are worth 2 Points each and work problems are 7 points each. How many of each type of equations are there?

Question

The next alAlgebra test is worth 100 points and contains 35 problems. Multiple-choice questions are worth 2 Points each and work problems are 7 points each. How many of each type of equations are there?

Answer 1

2x + 7y = 100

x + y = 35

x = 35 -y

2(35 - y) + 7y = 100

70 - 2y +7y = 100

70 + 5y =100

5y = 30

y = 6 questions

Therefore, there are 6 work problems at 7 points each, and:

x + 6 = 35

x = 29

29 multiple choice problems.

We can check our math with:

2(29) + 7(6) = 100

58 + 42 = 100

so we are correct.