Question

Find two consecutive even numbers where the sum of the smaller number and five times the larger number is equal to forty-six. What are the values of these two numbers?

Answer 1

The two consecutive even numbers that satisfy the given conditions are 6 and 8, with the smaller being 6 and the larger being 8.

Step-by-step explanation:

To find two consecutive even numbers where the sum of the smaller number and five times the larger number equals forty-six, let's represent the smaller number as n, and therefore the larger consecutive even number would be n + 2. We can set up the equation as follows:

n + 5(n + 2) = 46

Expanding the equation:

n + 5n + 10 = 46

Combining like terms gives us:

6n + 10 = 46

Subtracting 10 from both sides:

6n = 36

Dividing both sides by 6:

n = 6

Therefore, the smaller even number is 6. To find the larger one, we add 2:

6 + 2 = 8

So the two consecutive even numbers are 6 and 8.