Question

The average of 6 consecutive even numbers is 207. what will be the sum of the smallest and largest number?

Answer 1

x+(x+2)+(x+4)+(x+6)+(x+8)+(x+10))/6=207
6x+30=1242
6x=1212
x=1212/6=202
x+x+10=2x+10=2×202+10
=414

Answer 2

Given - Average

Find - Sum of smallest and largest number

Solution - Let the 6 consecutive even numbers be x, (x+2), (x+4), (x+6), (x+8) and (x+10).

Average = sum of all numbers/total numbers

Sum of all numbers = x + x+2 + x+4 + x+6 + x+8 + x+10

Performing addition

Sum of all numbers = 6x + 30

Keep the values in formula -

207 = (6x + 30)/6

6x + 30 = 207*6

Performing multiplication

6x + 30 = 1242

6x = 1242 - 30

Performing substraction

6x = 1212

x = 1212/6

Performing division

x = 202

Largest number = x + 10

Largest number = 202 + 10

Largest number = 212

Smallest number = x

Smallest number = 202

Sum = 202 + 212

Sum = 414

Hence, sum of the smallest and largest number as per the question is 414.