If the sum of three consecutive integers is 72, what is the smallest of these in

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Question: If the sum of three consecutive integers is 72, what is the smallest of these integers?

Options:

Correct Answer: 23

Solution:

Let the integers be x, x+1, and x+2. Their sum is x + (x + 1) + (x + 2) = 3x + 3 = 72. Solving gives 3x = 69, so x = 23.

If the sum of three consecutive integers is 72, what is the smallest of these integers?

If the sum of three consecutive integers is 72, what is the smallest of these integers?

Step 1: Understand that we need to find three consecutive integers. Let's call the first integer 'x'.
Step 2: The next two consecutive integers can be represented as 'x + 1' and 'x + 2'.
Step 3: Write an equation for the sum of these three integers: x + (x + 1) + (x + 2).
Step 4: Simplify the equation: x + x + 1 + x + 2 = 3x + 3.
Step 5: Set the equation equal to 72 because the sum is given as 72: 3x + 3 = 72.
Step 6: Subtract 3 from both sides of the equation to isolate the term with 'x': 3x = 72 - 3, which simplifies to 3x = 69.
Step 7: Divide both sides by 3 to solve for 'x': x = 69 / 3, which gives x = 23.
Step 8: The smallest of the three consecutive integers is 'x', which is 23.

Algebraic Expressions – Understanding how to represent consecutive integers using algebraic expressions.
Equation Solving – Solving linear equations to find the value of a variable.
Properties of Integers – Knowledge of how integers behave, particularly in sequences.