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Multiple-choice questions are worth 2 points each and word problems are worth 5 points. How many of each type of question are there? Your math teacher tells you that the next test is worth 100 points and contains 38 problems.

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Answer:

30 multiple choice and 8 word.

Step-by-step explanation:

m=multiple choice problem

w=word problem

2m+5w=100

m+w=38

2m+5w=100

2m+2w=76

Subtract

3w=24

w=8

38-8=30

Let MCQs be x and Word probs be y

  • x+y=38-(1)
  • 2x+5y=100-(2)

Multiply 2 with 1st eqn

[tex]\\ \sf\longmapsto 2x+2y=76[/tex]--(3)

Subtract eqn (2) and (3)

[tex]\\ \sf\longmapsto 3y=24[/tex]

[tex]\\ \sf\longmapsto y=8[/tex]

Put in first equation

[tex]\\ \sf\longmapsto 8+x=38[/tex]

[tex]\\ \sf\longmapsto x=30[/tex]

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