Answer:
5 multiple choice questions
Step-by-step explanation:
Write equations to represent the situation.
let "x" be the number of multiple choice questions
let "y" be the number of short answer questions
Equation for the total number of questions:
x + y = 20 # of multiple choice questions + # of short answer questions
Equation for the total points: (Multiply the type of question with how many points you get.)
x + 3y = 50 You don't need to write '1' beside 'x' for multiplying by 1.
The system of equations we need to solve is:
x + y = 20 and x + 3y = 50
We can solve using the substitution method.
Rearrange x + y = 20 to isolate one variable.
Isolate 'y'.
x + y = 20
x - x + y = 20 - x Subtract 'x' from both sides
y = 20 - x
Take the other equation x + 3y = 50. You can replace 'y' with the equation that equals 'y' that we got when rearranging.
Substitute y for 20 - x
x + 3y = 50
x + 3(20 - x) = 50 Use distributive property. Multiply the 3 outside the bracket by each number inside the bracket.
x + 60 - 3x = 50 Combine like terms. 'x' and '-3x' are alike because they both have 'x'.
60 - 2x = 50 Start isolating 'x'.
60 - 60 - 2x = 50 - 60 Subtract 60 from both sides.
-2x = 50 - 60 60-60 cancels out on the left side.
-2x = -10
-2x/-2 = -10/-2 Divide both sides by -2 to isolate 'x'.
x = -10/-2 -2x/-2 becomes 'x'. -2/-2 cancels out.
x = 5 Number of multiple choice questions
Therefore there are 5 multiple choice questions.
If you needed the number of short answer questions too, you would substitute x for 5 in any of the other equations.
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