When the smaller of two consecutive integers is added to four times the​ larger, the result is 44. Find the integers.

Answer 1

Let the smaller integer be \( x \). Since the integers are consecutive, the larger integer can be represented as \( x + 1 \).

According to the problem, when the smaller integer is added to four times the larger integer, the result is 44. This can be expressed with the equation:

\[ x + 4(x + 1) = 44 \]

Now, simplify the equation:

\[ x + 4x + 4 = 44 \]

Combine like terms:

\[ 5x + 4 = 44 \]

Next, subtract 4 from both sides:

\[ 5x = 40 \]

Now, divide by 5:

\[ x = 8 \]

Thus, the smaller integer is \( 8 \), and the larger integer (which is \( x + 1 \)) is:

\[ x + 1 = 9 \]

The two consecutive integers are \( 8 \) and \( 9 \).

To verify, substitute back into the original condition:

\[ 8 + 4(9) = 8 + 36 = 44 \]

Since this holds true, the integers are \( \boxed{8} \) and \( \boxed{9} \).