Question

1. a 50-point quiz has 15 questions. some are worth 4 points, some are worth 3 points. how many questions must be 4-point questions? a. 5 b. 10 c. 15 d. 20

Explanation:

Step1: Define variables

Let \( x \) be the number of 4 - point questions and \( y \) be the number of 3 - point questions. We know that the total number of questions is 15, so we have the equation \( x + y=15 \), which can be rewritten as \( y = 15 - x \). The total points of the quiz is 50, and the total points from 4 - point questions is \( 4x \) and from 3 - point questions is \( 3y \), so we have the equation \( 4x+3y = 50 \).

Step2: Substitute \( y \) into the point equation

Substitute \( y=15 - x \) into \( 4x + 3y=50 \). We get \( 4x+3(15 - x)=50 \).

Step3: Simplify and solve for \( x \)

First, expand the left - hand side: \( 4x+45 - 3x = 50 \). Then, combine like terms: \( x+45 = 50 \). Subtract 45 from both sides: \( x=50 - 45=5 \).

Answer:

A. 5