Question

8-43. find three consecutive numbers whose sum is 138 by writing and solving an equation.

Explanation:

Step1: Define the consecutive numbers

Let the first number be $x$. The three consecutive numbers are $x$, $x+1$, $x+2$.

Step2: Set up the sum equation

Sum equals 138, so:
$$x + (x+1) + (x+2) = 138$$

Step3: Simplify the left side

Combine like terms:
$$3x + 3 = 138$$

Step4: Isolate the variable term

Subtract 3 from both sides:
$$3x = 138 - 3$$
$$3x = 135$$

Step5: Solve for $x$

Divide both sides by 3:
$$x = \frac{135}{3} = 45$$

Step6: Find the other two numbers

Calculate $x+1$ and $x+2$:
$x+1 = 45+1=46$, $x+2=45+2=47$

Answer:

The three consecutive numbers are 45, 46, and 47.