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If the sum of three consecutive even integers is 78 , what is the first of the three even integers? (Hint: If x and x+2 represent the first two consecutive even integers, then how would the third consecutive even integer be represented?) The first of the three even integers is ◻

If the sum of three consecutive even integers is 7878 , what is the first of the three even integers? (Hint: If x x and x+2 x+2 represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)\newlineThe first of the three even integers is □ \square

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Full solution

Q. If the sum of three consecutive even integers is 7878 , what is the first of the three even integers? (Hint: If x x and x+2 x+2 represent the first two consecutive even integers, then how would the third consecutive even integer be represented?)\newlineThe first of the three even integers is □ \square
  1. Define First Even Integer: Let xx be the first even integer, then the second even integer is x+2x + 2 and the third is x+4x + 4 because even integers are 22 units apart.
  2. Calculate Sum of Consecutive Integers: The sum of these three consecutive even integers is x+(x+2)+(x+4)x + (x + 2) + (x + 4).
  3. Form Equation for Sum: The equation for the sum of the three integers is 3x+6=783x + 6 = 78.
  4. Isolate xx Term: Subtract 66 from both sides to isolate the term with xx: 3x=78−63x = 78 - 6.
  5. Solve for x: Calculate the right side: 3x=723x = 72.
  6. Calculate Final Value of x: Divide both sides by 33 to solve for x: x=723x = \frac{72}{3}.
  7. Calculate Final Value of x: Divide both sides by 33 to solve for x: x=723x = \frac{72}{3}.Calculate the value of x: x=24x = 24.

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