To find three consecutive integers whose sum is 48, we can set up an equation using algebra.

Step-by-Step Solution

1. Define the integers: Let the three consecutive integers be $x$, $x+1$, and $x+2$.

2. Set up the equation for their sum: $x + (x + 1) + (x + 2) = 48$

3. Combine like terms: $x + x + 1 + x + 2 = 48$ $3x + 3 = 48$

4. Isolate the variable term $3x$: $3x = 48 - 3$ $3x = 45$

5. Solve for $x$: $x = \frac{45}{3}$ $x = 15$

6. Determine the three consecutive integers: If $x = 15$, then the three consecutive integers are: $15, 16, \text{and } 17$

Final Answer

The three consecutive integers are 15, 16, and 17.

Would you like more details on any part of the solution, or do you have any questions?

Here are five related questions to consider:

1. How would the equation change if we wanted four consecutive integers with a sum of 100?
2. What if the problem asked for three consecutive even integers with a sum of 48? How would you solve it?
3. Can you explain why defining the integers as $x$, $x+1$, and $x+2$ is useful?
4. How can algebra be used to find integers that meet specific conditions, such as their sum or product?
5. What strategies are there for solving word problems involving integers in algebra?

Tip: When dealing with consecutive numbers, remember that their differences are consistent (e.g., 1 for consecutive integers, 2 for consecutive even or odd integers).