The sum of 3 consecutive even integers is 78. What is the largest of the integers?

is the sum 78 or 7,878 (i.e. was there a stutter)?

In any event, this sum must be even, so 3 consecutive even integers would be n, n+2 & n+4 whose sum is 3n + 6.

Set that to either 78 or 7878, whichever is intended, & solve for n.   If 78 is their grand total, then those 3 consecutive even numbers have to be 24, 26 & 28.

No stress!  Just logic! Keep the faith!

Step-by-step explanation:

28

Step-by-step explanation:

Let the first even integer be a.

The second even integer = a + 2

The third even integer = 2 + (a + 2) = a + 4

The sum of three consecutive even integers = 78

78 = a + (a + 2) + (a + 4)

78 = 3a + 6

72 = 3a

a = 24

The largest even integers is the third even integer = a + 4 = 24 + 4 = 28

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)