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(52903)   (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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