Question

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

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.

$\sf \implies \: 39 = \dfrac{8x + 4x + x}{3}$

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,

$\sf \implies \: 9 = x$

• 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.