Question

The sum of two numbers is 27. And their difference is three more than the smaller number. Find the number

Answer 1

Answer:

Required numbers are 8 and 19.

Step-by-step explanation:

Let,

Required numbers are a and b. { a > b }

Given that the sum of two numbers is 27. And their difference is three more than the smaller number.

Thus,

= > a + b = 27 ... ( 1 )

Also, a - b = b + 3

= > - b - b = 3 - a

= > - 2b = 3 - a

= > 3 + 2b = a

Substituting the value of a in ( 1 ) :

= > a + b = 27

= > 3 + 2b + b = 27

= > 3b = 27 - 3

= > b = 24 / 3

= > b = 8

Therefore,

= > a + b = 27

= > a + 8 = 27

= > a = 19

Hence the required numbers are 8 and 19.

Answer 2

Answer:

${\pink{\green{\sf{\therefore Greatest\:Number=19}}}}$

${\pink{\green{\sf{\therefore Smallest\:Number=8}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

▪In the given question information given about Relation between two Numbers and one number is Greater than other.

▪So we have to find those two Numbers by given data in question.

$\underline \bold{Given :} \\ \implies Let \: First \: Number = x \\ \implies Second\: Number = y \\ \implies x > y \\ \\ \underline \bold{ To \: Find : } \\ \implies First \: Number = ? \\ \implies Second \: Number = ?$

▪According to given question :

▪Form two eqn by given information.

$\implies x + y = 27 - - - - - (1)\\ \\ \implies x - y = y + 3 \\ \implies x - 2y = 3 - - - - - (2)$

▪Subtracting eqn (2) from eqn (1), We get

$\implies x - 2y - (x + y) = 3 - 27 \\ \implies x - 2y - x - x = - 24 \\ \implies - 3y = - 24 \\ \implies y = \frac{ 24}{3} \\ \bold{\implies y = 8} \\ \\ Putting \: value \: of \: y \: in \: (1) \\ \implies x + y = 27 \\ \implies x + 8 = 27 \\ \implies x = 27 - 8 \\ \bold{\implies x = 19}$

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