three consecutive integers have a sum of 48. find the integers.

Explanation:

Step1: Let the first integer be $x$.

The next two consecutive integers are $x + 1$ and $x+2$.

Step2: Set up the equation.

The sum of the three consecutive integers is $x+(x + 1)+(x+2)=48$.

Step3: Simplify the left - hand side of the equation.

Combining like terms, we get $3x+3 = 48$.

Step4: Solve for $x$.

Subtract 3 from both sides: $3x=48 - 3=45$. Then divide both sides by 3, so $x = 15$.

Step5: Find the other two integers.

The second integer is $x + 1=15 + 1 = 16$, and the third integer is $x+2=15 + 2=17$.

Answer:

15, 16, 17