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Three consecutive integers sum to 2424. Which integers are they?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_

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Full solution

Q. Three consecutive integers sum to 2424. Which integers are they?\newline_____\_\_\_\_\_, _____\_\_\_\_\_, _____\_\_\_\_\_
  1. Define Integers: Let xx be the first integer. The three consecutive integers can be represented as xx, x+1x+1, and x+2x+2.
  2. Set Up Equation: Set up the equation to represent the sum of the three consecutive integers equal to 2424: x+(x+1)+(x+2)=24x + (x+1) + (x+2) = 24.
  3. Simplify Equation: Simplify the equation: x+x+1+x+2=24x + x + 1 + x + 2 = 24. Combine like terms: 3x+3=243x + 3 = 24.
  4. Isolate Variable Term: Isolate the variable term by subtracting 33 from both sides of the equation: 3x+3−3=24−33x + 3 - 3 = 24 - 3. This simplifies to 3x=213x = 21.
  5. Divide to Solve: Divide both sides of the equation by 33 to solve for xx: 3x3=213\frac{3x}{3} = \frac{21}{3}. This gives us x=7x = 7.
  6. Find Consecutive Integers: Now that we have the value of xx, we can find the three consecutive integers: xx, x+1x+1, and x+2x+2. Substitute xx with 77: 77, 7+17+1, 7+27+2. This gives us the integers: 77, xx00, xx11.

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