Question

The average of 4 numbers is 360. If the three numbers are 320,350 and 400 find the fourth number.

Answer 1

GIVEN :–

• The average of 4 numbers is 360.

• The three numbers are 320,350 and 400.

TO FIND :–

• Fourth number = ?

SOLUTION :–

• Let the unknown number is 'x' .

• According to the question –

$\\ \bf \implies \dfrac{320 + 350 + 400 + x}{4} = 360$

$\\ \bf \implies 320 + 350 + 400 + x= 360 \times 4$

$\\ \bf \implies 320 + 350 + 400 + x=1440$

$\\ \bf \implies 350 + 720 + x=1440$

$\\ \bf \implies 1070 + x=1440$

$\\ \bf \implies x=1440 - 1070$

$\\ \large\implies{ \boxed{ \bf x=370}}$

• Hence , The unknown number is 370.

Answer 2

We have a formula for Calculating Average or Arithmetic Mean that is

$\boxed{\sf{Mean = \dfrac{\textsf{Sum of Observations}}{\textsf{No. of Observations}}}}$

But we are not calculating mean here, we are calculating for the fourth number. We are already given with the value of mean that is 360 and it is clear that No. of Observations = 4 from the Question! Since we do not know the value of fourth number, Consider it as "N"

$\implies\sf{360 = \dfrac{\textsf{320 + 350 + 400 + N}}{\textsf{4}}}$

$\implies\sf{360 = \dfrac{\textsf{1070 + N}}{\textsf{4}}}$

Apply Cross Multiplication [Where the Numerator of First fraction will be multiplied with the denominator of the fraction which is either side of the symbol "=" and Denominator of First fraction will be multiplied with the Numerator of the fraction which is either side of the symbol "="]

$\implies\sf{360 \times 4 = \textsf{1070 + N}}$

$\implies\sf{1440 = \textsf{1070 + N}}$

$\implies\sf{N = \textsf{1440 - 1070}}$

$\boxed{\boxed{\implies\sf{N = \textsf370}}}}$

Therefore, The fourth number is 370