Question

The sum of two numbers is 8 and their difference is 4.Find the number

Answer 1

✬ Numbers = 6 & 2 ✬

Step-by-step explanation:

Given:

• Sum of two numbers is 8.
• Their difference is 4.

To Find:

• What is the number ?

Solution: Let the two numbers be x and y. Therefore,

➼ First number + Second number = 8

➼ x + y = 8

➼ x = (8 – y)........(1)

Now,

➼ First number – Second number = 4

➼ x – y = 4......(2)

[ Putting the value of x in equation 2 ]

$\implies{\rm }$ x – y = 4

$\implies{\rm }$ 8 – y – y = 4

$\implies{\rm }$ 8 – 2y = 4

$\implies{\rm }$ – 2y = 4 – 8

$\implies{\rm }$ – 2y = – 4

$\implies{\rm }$ 2y = 4

$\implies{\rm }$ y = 2

So, numbers are

➭ Second number is y = 2

➭ First number is x = (8–y) = 8–2 = 6

Answer 2

• Given -

• The sum of two numbers is 8 and their difference is 4

• To Find -

• The No.

• Solution -

Let assume that two no.s be x & y respectively

★ Condition 1 -

Sum (+) of two no.s is 8

Let Frame Eqn for it,

$⟹x + y = 8$

$⟹x = 8 - y ... (1)$

★ Condition 2 -

Difference (-) of two no.s is 4

Let Frame Eqn for it,

★ Second no -

$⟹x - y = 4 ... (2)$

Placing value of x in eqn (2) ... (As it would be easier)

$⟹ x - y = 4$

$⟹8 - y - y = 4$

$⟹8 - 2y = 4$

$⟹ - 2y = 4 - 8$

$⟹ - 2y = - 4$

$⟹ y = \frac{\cancel{-4}}{\cancel{-2}}$

$⟹y = 2$

⛬ The second no. is 2

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

★ First no -

Placing y = 2 in eqn (1)

$⟹x = 8 - y$

$⟹x = 8 - 2$

$⟹x = 6$

⛬ First no. is 6

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Hence,

⛬ First no. is 6 & second no. is 2