Question

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.

Answer 1

Let MCQs be x and Word probs be y

• x+y=38-(1)
• 2x+5y=100-(2)

Multiply 2 with 1st eqn

`\\ \sf\longmapsto 2x+2y=76`--(3)

Subtract eqn (2) and (3)

`\\ \sf\longmapsto 3y=24`

`\\ \sf\longmapsto y=8`

Put in first equation

`\\ \sf\longmapsto 8+x=38`

`\\ \sf\longmapsto x=30`

Answer 2

30 multiple choice and 8 word.

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