Question

Find two consecutive even numbers whose sum is 758.

Answer 1

Explanation:

Let the first number = x

Let the second number = x + 2

x + x + 2 = 758 Collect like terms

2x + 2 = 758 Subtract 2

2x = 758 - 2 Combine

2x = 756 Divide by 2

2x/2 = 756/2

x = 378

The first number is 378

The second number 380

If your teacher is really fussy, you can do it this way.

Let the first number = 2x

Let the second number = 2x + 2

The reason for this is to guarantee that both numbers were even to start with.

2x + 2x+2 = 758 Combine like terms

4x + 2 = 758 Subtract 2

4x = 756 Divide by 4

x = 756/4

x = 189

Therefore 2x = 378

2x + 2 = 380 Just as before.

Answer 2

378 and 380

Explanation:

The two even consecutive numbers that add up to 758 are going to be very close to half of 758. This is because two half of 758 are going to be the most similar addends of 758. This is important because the answers will be consecutive and therefore, must also be very similar. To solve, first, divide 758 by 2. This is 379, which is not an even number. So, to find the needed addends subtract and add 1 to 379. Both of these will be even and consecutive. These two numbers are 378 and 380. Then, to check you, can add them and see that they do sum 758.