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?
Accepted Solution
A:
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.