Question

A math test is worth 100 points. There are a total of 26 questions. There are equation questions that are worth 2 points each and vocabulary questions are 5 points each. Use a system of equations to solve for the number of equation questions and vocabulary questions on the math test. Show all work for full credit.


WRITER

Answer 1

Let x = number of equation questions (2 points each) and y = number of vocabulary questions (5 points each).

Write the system:
1) x + y = 26
2) 2x + 5y = 100

Solve by substitution: from (1) x = 26 − y. Substitute into (2):
2(26 − y) + 5y = 100
52 − 2y + 5y = 100
52 + 3y = 100
3y = 48
y = 16

Then x = 26 − y = 26 − 16 = 10.

Check: 10·2 + 16·5 = 20 + 80 = 100.

Answer: 10 equation questions and 16 vocabulary questions.