Question

brandon has 132 petunia plants and 6 planters. he and his helpers will put x plants in each planter and have none left over. which of brandon’s three helpers, if any, correctly guessed how many plants are to be planted in each planter? use the equation (6x = 132).

helper	guess
bethany	25 plants
lacy	30 plants

Explanation:

Step1: Solve the equation \(6x = 132\)

To find the value of \(x\), we divide both sides of the equation by 6. So, \(x=\frac{132}{6}\)

Step2: Calculate the result

\(\frac{132}{6} = 22\). Wait, but looking at the guesses, maybe I misread. Wait, no, the equation is \(6x = 132\), so solving for \(x\): divide both sides by 6. \(x = 132\div6 = 22\). But the guesses are 20,25,30. Wait, maybe there's a mistake? Wait, no, let's check again. Wait, the problem says "Which of Brandon’s three helpers, if any, correctly guessed how many plants are to be planted in each planter? Use the equation \(6x = 132\)." So first, solve \(6x = 132\). Divide both sides by 6: \(x = 132/6 = 22\). But the guesses are Troy:20, Bethany:25, Lacy:30. Wait, none of them? But maybe I made a mistake. Wait, no, 622=132. So none of the helpers guessed correctly? But maybe the problem has a typo, or I misread. Wait, the original problem: Brandon has 132 petunia plants and 6 planters. He and his helpers will put x plants in each planter and have none left over. So solve 6x=132. x=22. So among Troy (20), Bethany (25), Lacy (30), none guessed 22. But maybe the equation was supposed to be different? Wait, maybe the user made a typo, but following the equation given: 6x=132, x=22. So none of the three helpers guessed correctly. But let's check the calculation again. 620=120, 625=150, 630=180. 622=132. So yes, x=22, so none of the three guessed correctly. But maybe the problem intended a different equation? Wait, maybe the equation was 6x=132, so x=22. So the answer is none, but the options given are the three guesses. Wait, maybe I misread the equation. Wait, the image shows "equation 6x = 132". So that's correct. So solving it, x=22. So none of Troy (20), Bethany (25), Lacy (30) guessed correctly. But maybe the problem has an error. Alternatively, maybe I made a mistake. Wait, 132 divided by 6: 620=120, 132-120=12, 12/6=2, so 20+2=22. Yes, x=22. So the correct guess would be 22, but none of the helpers guessed 22. But the problem asks "Which of Brandon’s three helpers, if any, correctly guessed...", so the answer is none, but since the options are the three, maybe there's a mistake. But following the equation, x=22, so none of Troy, Bethany, or Lacy guessed correctly.

Answer:

None of the three helpers (Troy, Bethany, Lacy) guessed correctly as the correct number of plants per planter is 22, and their guesses were 20, 25, and 30 respectively. But if we strictly follow the calculation from \(6x = 132\), \(x = 22\), so no helper guessed correctly.