Question

Sum of two numbers is 8. if the sum is four times their difference, find the numbers.

Answer 1

4+4=8 the word sum means addition

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

$\textbf{\underline{Two\;Numbers}}$

= p and c

Hence,

p + c = 8 ...... (1)

$\textbf{\underline{Sum\;is\;four\;times\;their \;difference}}$

Hence,

p + c = 4(p - c)

${\boxed{\sf\:{From\;(1)}}}$

8 = 4(p - c)

${\boxed{\sf\:{\dfrac{8}{4}=(p-c)}}}$

p - c = 2 ..... (2)

${\boxed{\sf\:{Now\;add\;(1)\;and\;(2)}}}$

p + c + p - c = 8 + 2

2p = 10

${\boxed{\sf\:{p=\dfrac{10}{2}}}}$

p = 5 ..... (3)

${\boxed{\sf\:{Substitute\;the\;value\;of\;(3)\;in\;(1)}}}$

p + c = 8

5 + c = 8

c = 8 - 5

c = 3

$\textbf{\underline{Therefore\;we\;get :-}}$

$\Large{\boxed{\sf\:{Two\;numbers\;are\;5\;and\;3}}}$