Question

The sum of three consecutive integers is 54. Write an equation to represent this relationship and solve for the unknown integers.

equation: x + (x+1) + (x+2) = 54
three integers: x, (x+1) and (x+2)

Answer 1

The equation for finding three consecutive integers that add up to 54 is x + (x+1) + (x+2) = 54. Solving for x, we find that x = 17, so the three integers are 17, 18, and 19.

Step-by-step explanation:

The student's question asks for an equation to find three consecutive integers that add up to 54. To represent the three consecutive integers, we generally use x, x+1, and x+2. The equation that represents the sum of these integers is:

x + (x+1) + (x+2) = 54

Combining like terms, we get:

3x + 3 = 54

To solve for x, we first subtract 3 from both sides:

3x = 54 - 3

3x = 51

Next, we divide both sides by 3 to isolate x:

x = 51/3

x = 17

Now that we have the value of x, we can find the three consecutive integers:

x = 17 (first integer)

(x + 1) = 17 + 1 = 18 (second integer)

(x + 2) = 17 + 2 = 19 (third integer)

Therefore, the three consecutive integers are 17, 18, and 19.