Question

1. 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
troy | 20 plants
bethany | 25 plants
lacy | 30 plants

Explanation:

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

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

Step2: Calculate the value of \(x\)

\(\frac{132}{6} = 22\). Now check the guesses: Troy guessed 20, Bethany 25, Lacy 30. Wait, but wait, maybe I miscalculated? Wait, no, 622=132. But the options given are 20,25,30. Wait, maybe there's a mistake? Wait, no, the problem says "use the equation 6x=132". Wait, maybe I misread. Wait, 6x=132, so x=22. But none of the helpers guessed 22? Wait, no, maybe the problem has a typo? Wait, no, let's check again. Wait, the problem says "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." Wait, but the guesses are 20,25,30. Wait, 620=120, 625=150, 630=180. None equal 132. Wait, that can't be. Wait, maybe the equation is wrong? Wait, no, the problem says to use 6x=132. Wait, maybe I made a mistake. Wait, 132 divided by 6 is 22. So none of the helpers guessed 22. But the problem says "if any". Wait, maybe the problem has a mistake, but according to the equation, x=22, so none of the helpers (Troy:20, Bethany:25, Lacy:30) guessed correctly? But that seems odd. Wait, maybe I misread the numbers. Let me check again. The plants are 132, planters 6. 132/6=22. The guesses are 20,25,30. So none of them. But maybe the problem meant 5x=132? No, the problem says 6x=132. So according to the equation, x=22, so none of the helpers guessed correctly. But let's confirm the calculations:

For Troy: 6*20=120 ≠132

For Bethany:6*25=150≠132

For Lacy:6*30=180≠132

So none of them. But maybe the problem has a typo, but based on the given equation, x=22, so none of the three helpers guessed correctly. Wait, but the problem says "if any". So the answer is none? But the options are their guesses. Wait, maybe I made a mistake in the equation. Wait, 6x=132, so x=22. So none of Troy (20), Bethany (25), Lacy (30) guessed 22. So the answer is none of them. But let's check again.

Wait, maybe the original problem had a different number of planters? No, it says 6 planters. So 6x=132, x=22. So none of the helpers guessed correctly. But the problem might have intended a different equation, but as per the given, none.

Answer:

None of the helpers (Troy: 20 plants, Bethany: 25 plants, Lacy: 30 plants) guessed correctly because solving \(6x = 132\) gives \(x = 22\), which is not among their guesses.