Question

Mrs. Simmons gave a history test worth 92 points. There were only two types of questions on it: 2-point true/false questions and 5-point fill-in-the-blank questions. If there were a total of 34 questions on the test, how many of them were true/false? How many were fill in the blank?

Please show your work from your solving portion of the answer...

Answer 1

There are 8 true/false questions and 26 fill-in-the-blank questions.

Explanation:

Let "t" be the number of 2-point true/false questions and "f" the number of 5-point fill-in-the-blank questions.

Mrs. Simmons gave a history test worth 92 points. Symbollically,

2 t + 5 f = 92 [1]

There were a total of 34 questions in the test. Symbollicaly,

t + f = 34

t = 34 - f [2]

If we replace [2] in 1, we get

2 (34 - f) + 5 f = 92

68 - 2 f + 5 f = 92

3 f = 24

f = 8

We replace f = 8 in [2],

t = 34 - 8 = 26

There are 8 true/false questions and 26 fill-in-the-blank questions.