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The sum of three consecutive even integers is 54 . Find the value of the least of the three. Answer:

The sum of three consecutive even integers is 5454 . Find the value of the least of the three.\newlineAnswer:

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Full solution

Q. The sum of three consecutive even integers is 5454 . Find the value of the least of the three.\newlineAnswer:
  1. Define First Even Integer: Let xx be the first even integer. \newlineWhich represents the three consecutive even integers?\newlineConsecutive even integers increase by 22 each time. \newlineConsecutive even integers: xx, x+2x+2, x+4x+4
  2. Sum of Consecutive Integers: Which equation represents the sum of 33 consecutive even integers is 5454?\newlineAdd three consecutive even integers and equate the sum to 5454.\newlineEquation: x+(x+2)+(x+4)=54x + (x+2) + (x+4) = 54
  3. Simplify Equation: Simplify the left side of x+(x+2)+(x+4)=54x + (x+2) + (x+4) = 54.
    x+(x+2)+(x+4)=54x + (x+2) + (x+4) = 54
    (x+x+x)+(2+4)=54(x + x + x) + (2+4) = 54
    3x+6=543x + 6 = 54
  4. Isolate Variable Term: Isolate the variable term in 3x+6=543x + 6 = 54.
    3x+6=543x + 6 = 54
    3x+6−6=54−63x + 6 - 6 = 54 - 6
    3x=483x = 48
  5. Solve for x: Solve for x.\newline3x=483x = 48 \newline3x3=483\frac{3x}{3} = \frac{48}{3} \newlinex=16x = 16
  6. Find Least Integer: We have: \newlinex=16x = 16 \newlineWhat is the value of the least of the three consecutive even integers?\newlineThe least integer is xx, which is 1616.

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