Question

1) 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 Marry is 35.6kg.
• The Average mass of jane and Peter is 36 kg .

To Find,

• The Mass of Mary.

Solution,

⇒Suppose the Mass of Jane be a years

And, Suppose the Mass of Peter be b years

And, Suppose the Mass of Mary be c years

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• The Average mass of Jane,Peter and Marry is 35.6 kg

$\implies \boxed{\sf{Average \ Mass = \dfrac{Sum \ of \ three \ mass }{Total \ Number\ of \ mass}}}$

$\implies \sf{\dfrac{a + b + c}{3} = 35.6}$

$\implies \sf{a + b + c = 35.6 \times 3}$

$\implies \sf{a + b + c = 106.8}$

$\implies \sf{a + b = 106.8 - c}$

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• The Average mass of Jane and Peter is 36kg

$\implies \sf{\dfrac{a + b}{2} = 36}$

$\implies \sf{a + b = 36 \times 2}$

$\implies \sf{a + b = 72}$

Now We Put the value of (a + b) in Second  Condition :-

$\implies \sf{106.8 - c = 72}$

$\implies \sf{106.8 - 72 = c}$

$\implies \boxed{\sf{c = 34.8}}$

Therefore,

$\boxed{\bold{\red{Mass \ of \ Mary = c = 34.8 \ kg}}}$

$\rule{200}2$

Answer 2

Given

Average mass of Jane, Peter & Mary = 35.6 kg.

Average mass of Jane & Peter = 36 kg.

To find

Mass of Mary

Solution

Here, let the masses of Jane, Peter & Mary be x, y & z kg respectively.

As we know,

➥ Average mass = Total masses/Number of people.

According to Question :

➝ (x + y + z)/3 = 35.6

➝ x + y + z = 3 × 35.6

➝ x + y + z = 106.8 -(Eq.1)

Case 2 :

⟼ (x + y)/2 = 36

⟼ x + y = 36 × 2

⟼ x + y = 72 -(Eq.2)

Now putting value of (Eq.2) in (Eq.1)

➻ 72 + z = 106.8

➻ z = 106.8 - 72

➻ z = 34.8 kg

Therefore,

Mass of Mary = 34.8 kg.