Question

Ms. miller decides to give a test worth 90 points and contains 25 questions. multiple-choice questions are worth 3 points and word problems are worth 4 points. how many of each type of question are there?

Answer 1

X= # of multiple choice questions
y= # of word problem questions

EQUATION 1:
x + y= 25

EQUATION 2:
3x + 4y= 90


STEP 1:
solve for one variable in equation 1

x + y= 25
subtract y from both sides
x= 25 - y


STEP 2:
substitute x=25-y in equation 2

3x + 4y= 90
3(25-y) + 4y= 90
75 - 3y + 4y= 90
75 + y= 90
subtract 75 from both sides
y= 15 word problems


STEP 3:
substitute y value to find x

x + y= 25
x + 15= 25
x= 10 multiple choice questions


ANSWER: There are 15 word problems and 10 multiple choice questions.

Hope this helps! :)

Answer 2

m + w = 25

3m + 4w = 90

 

Let's do substitution, first by solving the first equation for m.

 

m = 25 - w

 

Substitute!

 

3(25 - w) + 4w = 90

75 - 3w + 4w = 90

w = 15

 

m = 25 - 15 = 10

 

Hope this helps!