Question

the sum of three consecutive even numbers is 24 more than the average of the numbers.what is third largest number

Answer 1

the third largest number will be 14

Answer 2

Answer:

14

Step-by-step explanation:

Let the three consecutive even numbers be x,x+2,x+4

Sum of three consecutive even numbers = $x+x+2+x+4$

                                                                    = $3x+6$

Average of three consecutive even numbers = $\frac{\text{Sum of all numbers}}{\text{Total numbers}}$

                                                                            $=\frac{x+x+2+x+4}{3}$

                                                                           $=\frac{3x+6}{3}$

Now we are given that the sum of three consecutive even numbers is 24 more than the average of the numbers.

So,$3x+6=\frac{3x+6}{3}+24$

[tex]3x+6-24=\frac{3x+6}{3}[\tex]

[tex]3x-18=\frac{3x+6}{3}[\tex]

[tex]3(3x-18)=3x+6[\tex]

[tex]9x-54=3x+6[\tex]

[tex]6x=60[\tex]

[tex]x=10[\tex]

Thus the third largest number =x+4=10+4=14

Hence third largest number is 14