Answer :

To find four consecutive integers that add up to 186, we can solve it step-by-step like this:

1. Define the Integers: Let's call the first integer [tex]\( x \)[/tex]. Since the integers are consecutive, the next three integers will be [tex]\( x+1 \)[/tex], [tex]\( x+2 \)[/tex], and [tex]\( x+3 \)[/tex].

2. Set Up the Equation: According to the problem, their sum is 186. So, we can write the equation:
[tex]\[
x + (x + 1) + (x + 2) + (x + 3) = 186
\][/tex]

3. Simplify the Equation: Combine like terms:
[tex]\[
x + x + 1 + x + 2 + x + 3 = 186
\][/tex]
[tex]\[
4x + 6 = 186
\][/tex]

4. Solve for [tex]\( x \)[/tex]:
- Subtract 6 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
4x = 180
\][/tex]
- Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 45
\][/tex]

5. Find All Four Integers: Now that we know [tex]\( x = 45 \)[/tex], we can find the four consecutive integers:
- First integer: [tex]\( 45 \)[/tex]
- Second integer: [tex]\( 45 + 1 = 46 \)[/tex]
- Third integer: [tex]\( 45 + 2 = 47 \)[/tex]
- Fourth integer: [tex]\( 45 + 3 = 48 \)[/tex]

Therefore, the four consecutive integers are 45, 46, 47, and 48.

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