The sum of two numbers is 46. The larger number is 6 more than the smaller number. What are the numbers?

1 answer

Let the smaller number be \( x \). According to the problem, the larger number is \( x + 6 \).

We know from the problem that the sum of the two numbers is 46, so we can set up the equation:

\[ x + (x + 6) = 46 \]

Now, simplify and solve for \( x \):

\[ 2x + 6 = 46 \]

Subtract 6 from both sides:

\[ 2x = 40 \]

Now, divide by 2:

\[ x = 20 \]

Now that we have the smaller number, we can find the larger number:

\[ x + 6 = 20 + 6 = 26 \]

Thus, the two numbers are:

  • Smaller number: \( 20 \)
  • Larger number: \( 26 \)

In conclusion, the numbers are 20 and 26.