Question

Find 2 numbers with a mean of 14 and a difference of 4

Answer 1

Given: Mean is 14; difference between the numbers is 4.

To find: The two numbers.

Answer:

Let one number be x and the other be y.

$\tt Mean\ =\ \dfrac{Sum\ of\ the\ observations}{Total\ number\ of\ observations}$

We have mean = 14. Total number of observations is 2 [as per the question.]

Therefore,

$\tt 14\ =\ \dfrac{x\ +\ y}{2}\\\\\\28\ =\ x\ +\ y$

Now, again, as per the question, x - y = 4.

x + y = 28

x - y = 4

On solving these equations, we get x = 16 and y = 12.

Therefore, the two numbers are 16 and 12.

Answer 2

$\huge\bold\green{Question}$

Find 2 numbers with a mean of 14 and a difference of 4

$\huge\bold\green{Answer}$

According to the question we have :-

°•° mean = 14

°•° Difference bw. numbers = 4

Now , we have find the two numbers

Let one number be “ a ” and the other be “ b ”

$\sf\boxed{Mean\ =\ \dfrac{Sum\ of\ the\ observations}{Total\ number\ of\ observations}}$

Hence we have mean = 14 and the total number of observations is 2

So,

$\begin{lgathered}\sf\implies 14\ =\ \dfrac{a\ +\ b}{2}\\\\\\\sf\implies28\ =\ a\ +\ b\end{lgathered}$

Now, as said in question a - b = 4.

→ a + b = 28 ____________(1)

→ a - b = 4 _____________(2)

So, by solving eqn (1) and (2), we get correct values

→ a = 16

→ b = 12.

Hence the two required numbers are 16 and 12