SOLUTION: A test has 18 problems, which are worth a total of 111 points. There are two types of problems in the test. Each multiple-choice problem is worth 5 points, and each short-answer pr

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Question 1188845: A test has 18 problems, which are worth a total of 111 points. There are two types of problems in the test. Each multiple-choice problem is worth 5 points, and each short-answer problem is worth 8 points. Write and solve a system equation to figure out how many multiple choice problems and short-answer problems.

Answer by ikleyn(52785)   (Show Source): You can put this solution on YOUR website!
.
The system of equations is


      x +  y =  18    (1)    (counting problems)

     5x + 8y = 111    (2)    (counting points)


You can solve it by many methods (Substitution, Elimination, determinants).


Substitution method gives  x = 18-y, and then from equation (2)


    5(18-y) + 8y = 111

    90 - 5y + 8y = 111

           3y    = 111 - 90 = 21

            y               = 21/3 = 7.


ANSWER.  7 short-answer problems and 18-7 = 11 multiple choice problems.


CHECK.  7*8 + 11*5 = 56 + 55 = 111 points, in total.   ! Correct !

Solved.



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