Question

1. a 40-question test has 132 possible points. there are m 5-point questions and n 1-point questions. how many of each type of question is on the test? a m=23, n=17 b m=25, n=25 c m=30, n=20 d m=35, n=15

Explanation:

Step1: Set up equations

We know two things: the total number of questions is 40, so \( m + n = 40 \). The total points are 132, with \( m \) questions worth 5 points and \( n \) worth 1 point, so \( 5m + n = 132 \).

Step2: Solve the system of equations

Subtract the first equation from the second: \( (5m + n) - (m + n) = 132 - 40 \). Simplify: \( 4m = 92 \), so \( m = \frac{92}{4} = 23 \). Then substitute \( m = 23 \) into \( m + n = 40 \): \( 23 + n = 40 \), so \( n = 40 - 23 = 17 \).

Step3: Check the options

Option A has \( m = 23 \), \( n = 17 \), which matches our solution.

Answer:

A. \( m = 23, n = 17 \)