Question

The average of four consecutive even numbers is 35 find the smallest of four numbers

Answer 1

Answer:

32

Step-by-step explanation:

Average = sum of the observations / Number of observations

Let the first even number be a

the three consecutive numbers are a+ 2 , a+4, a+6

average of 4 consecutive even numbers = 35

here sum of observations = a + a+2 + a+4 + a+6 = 4a + 12 = 4 ( a+ 3)

number of observations = 4

⇒Average =  sum of observations / number of observations  = 35

⇒ 4 ( a + 3)  / 4 = 35

⇒ a + 3 = 35

⇒ a = 35 - 3

⇒ a = 32

the numbers are a = 32

a+2 = 32 + 2 = 34

a+4 = 32 + 4 = 36

a+6 = 32 + 6 = 38

the smallest number is 32

Answer 2

Given: The average of four consecutive even numbers is $35.$

We have to find the smallest of four numbers.

Let, the 4 consecutive even numbers be $2 n, 2 n+2,2 n+4,2 n+6$

We have the average of these four consecutive even numbers is$35$.

i.e.

$=>\frac{(2 n)+ (2 n+2)+(2 n+4)+(2 n+6)}{4} =35\\\\=>\frac{2[(n)+(n+1)+(n+2)+(n+3)] }{4}=35 \\\\=>\frac{[(n)+(n+1)+(n+2)+(n+3)]}{2} =35$        

$=>[(n)+(n+1)+(n+2)+(n+3)]=70\\=>4 n+6=70\\=>4n=70-6\\=>4n=64\\=>n=\frac{64}{4} \\\\=>n=16$

So, the four consecutive even numbers will be,

$=>2\times16=32\\=>2\times16+2=34\\=>2\times16+4=36\\=>2\times16+6=38$

Hence, the smallest number will be$32.$