Question

Q1.The average of three numbers is 39.If the first number is twice the second and the the second is four times the third find the number

Answer 1

Explanation:

Given:

Three numbers -

First Number

Second Number

Third Number

With -

Average = 39

What To Find:

We have to find -

The third number.

Solution:

Forming the equation.

Here it is given that -

First number = 2 × Second Number

Second number = 4 × Third Number

Let's take -

Third number = x

So -

Second number = 4 × x = 4x

First number = 2 × 4x = 8x

We know that -

Average = Sum of observations ÷ Number of observations

That is -

Average = 39

Sum of observations = 8x + 4x + x

Number of observations = 3

Thus, the equation is -

$\bf \to \: 39 = \dfrac{8x + 4x + x}{3}$

Solving the equation.

$\sf \implies \: 39 = \dfrac{8x + 4x + x}{3}</p><p>$

Add the numerator,

$\sf \implies \: 39 = \dfrac{13x}{3}$

Take 3 to LHS from RHS,

$\sf \implies \: 39 \times 3 = 13x$

Multiply 39 by 3 in LHS,

$\sf \implies \: 117 = 13x$

Take 13 to LHS from RHS,

$\sf \implies \: \dfrac{117}{13} = x$

Divide 117 by 13,

9=x

Substituting the values.

Here -

First number = 8x = 8 × 9 = 72

Second number = 4x = 4 × 9 = 36

Third number = x = 9

Final Answer:

∴ Thus, the third number is 9.