How do you find three consecutive even numbers whose sum is 54?

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Answer 1 · 2016-11-15T08:09:06

The three numbers are $16$ $16$ , $18$ $18$ , and $20$ $20$ .

We shall represent the three consecutive even numbers by $x$ $x$ , $(x + 2)$ $(x+2)$ and $(x + 4)$ $(x+4)$ . An equation can be written:

$x + (x + 2) + (x + 4) = 54$ $x+ (x+2)+(x+4)=54$

Open the brackets and simplify.

$x + x + 2 + x + 4 = 54$ $x+ x+2+x+4=54$

$3 x + 6 = 54$ $3x+6=54$

Subtract $6$ $6$ from each side.

$3 x = 48$ $3x=48$

Divide both sides by $3$ $3$ .

$x = 16$ $x=16$

$:. (x+2)=18$ and $(x+4)=20$