Mr. Lopez wrote the equation 32 g + 8 g minus 10 g = 150 on the board. Four students explained how to solve for g.

Question

Alyssa: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then subtracted 30 from 150 to find the value of g, which is 120.”

Rahul: “I added 32, 8, and 10 to get 50, and then I subtracted 150 to find the value of g, which is –100.”

Toni: “I subtracted 18 from 32 to get 14, which I then divided into 150 to find the value of g, which is 10 and StartFraction 5 Over 7 EndFraction.”

Wilhem: “I added 32 and 8 to get 40, subtracted 10 to get 30, and then divided both sides by 30 to find the value of g, which is 5.”

Which student’s work is correct?
Alyssa
Rahul
Toni
Wilhem

Answer 1

Let's start by simplifying the equation \(32g + 8g - 10g = 150\).

Combine like terms on the left side:

\[ (32g + 8g - 10g) = 150 \] \[ (32g + 8g = 40g) - 10g = 30g \] So, we have: \[ 30g = 150 \]

Now, to solve for \(g\), divide both sides by 30:

\[ g = \frac{150}{30} = 5 \]

Now let's evaluate each student's explanation:

1. Alyssa: She states she got \(g = 120\). This is incorrect.
2. Rahul: He states he got \(g = -100\). This is incorrect.
3. Toni: She claims her answer is \(g = 10 \frac{5}{7}\). This is incorrect.
4. Wilhem: He states he got \(g = 5\). This is correct.

Thus, the only student with the correct solution is Wilhem.