Question

the greater of two numbers is 12 more than the smallest and the sum of the two numbers is 10 find the number​

Answer 1

Answer:

Given :

• The greater of two numbers is 12 more than the smaller and the sum of the two numbers is 10.

To Find :-

• What are the numbers.

Solution :-

Let,

➲ Smaller Number = x

➲ Greater Number = x + 12

According to the question,

⇒ x + (x + 12) = 10

⇒ x + x + 12 = 10

⇒ 2x + 12 = 10

⇒ 2x = 10 - 12

⇒ 2x = - 2

⇒ x = - 2/2

➦ x = - 1

Hence, the required numbers are :

❒ Smaller Number :

↦ Smaller Number = x

➠ Smaller Number = - 1

❒ Greater Number :

↦ Greater Number = x + 12

↦ Greater Number = - 1 + 12

➠ Greater Number = 11

∴ The numbers are - 1 and 11.

VERIFICATION :-

⇒ x + x + 12 = 10

By putting x = - 1 we get,

⇒ - 1 + (- 1) + 12 = 10

⇒ - 1 - 1 + 12 = 10

⇒ - 2 + 12 = 10

➭ 10 = 10

Hence, Verified.

Answer 2

${{ \boxed{\boxed{\begin{array}{cc} \maltese  \bf \:Let \\ \\ \rm \to \: the \: smaller \: number \: be \: X \\ \\ \rm and \\ \\ \to \rm the \: greater \: number \: be \: Y \\ \\ \\ \bf \: given \\ \\ \rm \to \: The \: greate r \: number \: is \: 12 \\ \rm more \: than \: the \: smaller \: number. \\ \\ => Y = X + 12 \: \: \: \: - - - - (1)\\ \\ \rm Also, \: sum \: of \: the \: number \: i s \: = 10\\ \\ => X + Y = 10 \: \: \: - - - - (2) \\ \\ \rm \: Substitute \: eqn.(1) \: in \: eqn.(2) \: \\ \rm \: we \: will \: get, \\ \\ => X + (X +12) = 10 \\ \\ => X + X + 12 =10 \\ \\ => 2X = 10–12 \\ \\ = 2X = -2 \\ \\ => X = -1. \\ \\ \\ \rm \: Substitute \: the \: value \: of \: X \\ \rm in \: eqn.(1) \: we \: will \: g et, \\ \\ Y = -1+12 = 11. \\ \\ \rm \: Therefore \: the \: numbers \: are \: \: -1 \: \\ \rm \: and \: \: 11. \: \: \end{array}}}}}$