Problem Breakdown: Consecutive Multiples of 2

We are asked to find the largest of five consecutive multiples of 2, given that their sum is 660.

Setting Up the Algebraic Equation

Let the five consecutive multiples of 2 be represented algebraically. If we denote the middle multiple as x, the sequence can be written as:

• x - 4
• x - 2
• x
• x + 2
• x + 4

The sum of these five consecutive multiples is given as 660. We can write this as an equation:

$ (x - 4) + (x - 2) + x + (x + 2) + (x + 4) = 660 $

Solving for the Middle Multiple

Simplify the equation by combining like terms:

$ 5x = 660 $

Now, solve for x by dividing both sides by 5:

$ x = \frac{660}{5} $

$ x = 132 $

So, the middle multiple of 2 is 132.

Finding the Largest Multiple

The five consecutive multiples are:

• 132 - 4 = 128
• 132 - 2 = 130
• 132
• 132 + 2 = 134
• 132 + 4 = 136

The largest number in this sequence is x + 4.

$ \text{Largest Number} = 132 + 4 = 136 $

The largest number among the five consecutive multiples of 2 is 136.