Solve using substitution ot elimination

Question

On a math test, seven points will be taken off for every wrong answer and five points will be added for every correct answer. If you answer all 24 questions, and get a score of zero. How many questions were correct and how many were wrong.

Answer 1

Let c represent correct answers and i represent incorrect answers.

The sum of correct and incorrect answers equals 24 total answers:

c + i = 24

The correct answers multiplied by 5 points minus the incorrect answers multiplied by 7 points equals a total score of 0:

5c - 7i = 0

With two equations we can solve for two variables:

c + i = 24

c = 24 - i

Plug this into the other equation for c:

5(c) - 7i = 0

5(24 - i) - 7i = 0

120 - 5i -7i = 0

120 - 12i = 0

-12i = -120

i = 10

Now plug this value for i into either original equation:

c = 24 - 10 = 14