Question

The average mass of Jane,Peter and Mary is 35.6kg.And the average mass of Jane and Peter is 36kg.What is the mass of Mary?

Answer 1

Given :

• The average mass of Jane,Peter and Mary is 35.6kg.
• And the average mass of Jane and Peter is 36kg.

To Find :

• Mass of Mary.

Solution :

Let x be the mass of Jane.

Let y be the mass of Peter.

Let z be the mass of Mary.

Case 1 :

Average mass of all three → 35.6 kg.

Equation :

$\longrightarrow$ $\sf{\dfrac{x+y+z}{3}\:=35.6}$

$\longrightarrow$ $\sf{x+y+z=106.8}$

$\sf{x+y=106.8-z}$ ____(1)

Case 2 :

Average mass of Jane and Peter is 36 kg.

Equation :

$\longrightarrow$ $\sf{\dfrac{x+y}{2}=36}$

$\longrightarrow$ $\sf{x+y=72}$

From equation (1), we can replace (x+y),

$\longrightarrow$ $\sf{106.8-z=72}$

$\longrightarrow$ $\sf{106.7-72=z}$

$\longrightarrow$ $\sf{34.8=z}$

$\large{\boxed{\sf{\red{Mass\:of\:Mary\:=\:z\:=\:34.8\:kg}}}}$