Question

three good friends are in the same algebra class. their scores on a recent test are three consecutive integers whose sum is 276. find each score. (use commas to separate answers.)

Explanation:

Step1: Define variables for scores

Let the three consecutive integers be \( x \), \( x + 1 \), and \( x + 2 \).

Step2: Set up the equation

The sum of these three integers is 276, so we have the equation:

$$ x + (x + 1) + (x + 2) = 276 $$

Step3: Simplify the left - hand side

Combine like terms:

$$ x+x + 1+x + 2=3x+3 $$

So the equation becomes \( 3x + 3=276 \).

Step4: Solve for x

Subtract 3 from both sides:

$$ 3x=276 - 3=273 $$

Divide both sides by 3:

$$ x=\frac{273}{3}=91 $$

Step5: Find the other two scores

If \( x = 91 \), then \( x + 1=91 + 1 = 92 \) and \( x + 2=91+2 = 93 \).

Answer:

The three scores are 91, 92, and 93.