The Correct Answer and Explanation is:
The correct answer is: Subtract 6 from 27, then divide by 3.
Here is an explanation of how to arrive at this answer.
To solve this word problem, we first need to translate the sentence into a mathematical equation. Let’s use the variable ‘b’ to represent Brandon’s age.
The problem states, “His age [Sam’s age] is 6 years greater than 3 times Brandon’s age.” Let’s break this down:
- “3 times Brandon’s age” can be written as 3 * b or 3b.
- “6 years greater than” means we add 6 to the previous expression. This gives us 3b + 6.
- We are told that this expression is equal to Sam’s age, which is 27. So, the complete equation is 3b + 6 = 27.
Now, the goal is to find Brandon’s age, which means we need to solve the equation for ‘b’. To do this, we use inverse operations to isolate the variable ‘b’. We must reverse the order of operations (PEMDAS in reverse).
- Undo the addition: The equation has a “+ 6”. To undo this, we subtract 6 from both sides of the equation:
3b + 6 – 6 = 27 – 6
3b = 21
This first step is described as “Subtract 6 from 27”. - Undo the multiplication: The equation now has ‘b’ multiplied by 3. To undo this, we divide both sides of the equation by 3:
3b / 3 = 21 / 3
b = 7
This second step is described as “then divide by 3”.
Therefore, the correct sequence of steps to find Brandon’s age is to first subtract 6 from 27 and then divide the result by 3. This matches the chosen answer perfectly. The other options are incorrect because they represent different equations or an incorrect order of operations for solving the problem.
