Mrs. McAlister wrote the equation 10 t minus 4 t + 3 t = 8 on the board and asked students to write an equivalent equation. The table below shows the responses from four students.

Question

Student Responses
Name
Equation
Michele
3 t = 8
Piotr
6 t = 8
Ronnie
Negative 1 t = 8
Tanisha
9 t = 8

Which student wrote an equation that is equivalent to Mrs. McAlister’s?
Michele
Piotr
Ronnie
Tanisha

Answer 1

Let's simplify Mrs. McAlister's equation step by step:

The original equation is:

\[ 10t - 4t + 3t = 8 \]

First, let's combine the like terms on the left side:

1. Combine \(10t\) and \(-4t\): \[ 10t - 4t = 6t \]

2. Now we have: \[ 6t + 3t = 8 \]

3. Combine \(6t\) and \(3t\): \[ 6t + 3t = 9t \]

So we simplify the equation to:

\[ 9t = 8 \]

Now let's compare this with the equations given by each student:

• Michele: \(3t = 8\) - Not equivalent
• Piotr: \(6t = 8\) - Not equivalent
• Ronnie: \(-1t = 8\) - Not equivalent
• Tanisha: \(9t = 8\) - Equivalent

Therefore, the student who wrote an equation that is equivalent to Mrs. McAlister’s is Tanisha.