Question

In a set of four integers, the average of the two smallest integers is 102, the average of the three smallest integers is 103, the average of all four is 104. Which is the greatest of these integers?​

Answer 1

Step-by-step explanation:

Given :-

The average of the two smallest integers is 102.

The average of the three smallest integers is 103 .

The average of all four integers is 104.

To find :-

The greatest integer .

Solution :-

Let the four integers be a,b,c and d

Let a < b < c < d

The smallest integer = a

The greatest integer = d

We know that

Average = Sum of all observations / Number of all observations

Average of two smallest integers = 102

=> (a+b)/2 = 102

=> a+b = 102×2

=> a+b = 204 --------------(1)

Given that

The average of the three smallest integers = 103

=> (a+b+c)/3 = 103

=> a+b+c = 103×3

=> a+b+c = 309 ----------(2)

From (1) , equation (2) becomes

=> 204+c = 309

=> c = 309-204

=> c = 309-204

=> c = 105

Therefore, c = 105

Given that

Average of four integers = (a+b+c+d)/4

According to the given problem

Average of all four integers = 104

=> (a+b+c+d)/4 = 104

=> a+b+c+d = 104×4

=> a+b+c+d = 416 ------(3)

Therefore ,

Sum of all four integers = 416

On substituting the value of (a+b+c) in (3) then

=> 309+d = 416

=> d = 416 - 309

=> d = 107

Therefore, the greatest integer = 107

Answer :-

The greatest integer among all the four integers is 107.

Used formulae :-

Average = Sum of all observations /Number of all observations

Answer 2

QUESTION :

• In a set of four integers, the average of the two smallest integers is 102, the average of the three smallest integers is 103, the average of all four is 104. Which is the greatest of these iintegers

GIVEN :

• the average of the two smallest integers is 102, the average of the three smallest integers is 103the average of all four is 104

TO FIND :

• Which is the greatest of these integers = ?

SOLUTION :

in these questions we have PQRS and

we have greater number is S. and small number is P

first we have :

• P + Q /2 = 102

• P + Q = 204

then we have :

• P + Q + R /3 = 103

• P + Q + R = 309

then, we have :

• P + Q + R + S /4 = 104

• P + Q + R + S = 416

• 309 + S = 416

then, we will minus then, we will get the answer :

• S = 416 - 309

we get answer :

• = 107

so, we have greatest integer = 107