Question

four more than half of the students in bryans homeroom have tickets to attend the schools musical. 20 students have tickets. select all the equations that can be used to find the number of students in bryans homeroom.
a. $4 - \frac{1}{2}m = 20$

b. $\frac{1}{2}m + 4 = 20$

c. $\frac{1}{2}m - 4 = 20$

d. $4 = 20 - \frac{1}{2}m$

e. $20 + \frac{1}{2}m = 4$

Explanation:

Step1: Define the variable

Let \( m \) be the number of students in Bryan's homeroom.

Step2: Translate the problem into an equation

"Half of the students" is \( \frac{1}{2}m \), "four more than half of the students" is \( \frac{1}{2}m + 4 \). We know that this is equal to 20 (the number of students with tickets), so the equation is \( \frac{1}{2}m + 4 = 20 \) (which is option B).

We can also rearrange this equation. Subtract \( \frac{1}{2}m \) from both sides: \( 4 = 20 - \frac{1}{2}m \) (which is option D).

Let's check the other options:

• Option A: \( 4 - \frac{1}{2}m = 20 \) would mean 4 minus half the students is 20, which does not match the problem statement.
• Option C: \( \frac{1}{2}m - 4 = 20 \) would mean half the students minus 4 is 20, which is not what the problem says.
• Option E: \( 20 + \frac{1}{2}m = 4 \) would mean 20 plus half the students is 4, which is impossible in this context.

Answer:

B. \(\frac{1}{2}m + 4 = 20\), D. \(4 = 20 - \frac{1}{2}m\)