Question

if 45 is subtracted from twice the great er of two numbers, it result in the other number. if 21is subtract from twice the smaller number ,it resulted in the greatest number. find the number
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Answer 1

EXPLANATION.

Let x be the greater number and y be the

smaller number.

To find the number.

According to the question,

Case = 1.

if 45 is subtracted from twice the greater

of two number.

=> 2x - 45 = y .........(1)

Case = 2.

if 21 is subtracted from twice the smaller

number it resultant in the greatest number.

=> x = 2y - 21 ......(2)

From equation (1) and (2) we get,

=> put the value of Equation (2) in (1)

we get,

=> 2 ( 2y - 21 ) - 45 = y

=> 4y - 42 - 45 = y

=> 3y - 87 = 0

=> y = 29

put the value of y = 29 in equation (2)

we get,

=> x = 2 ( 29 ) - 21

=> x = 58 - 21

=> x = 37

Therefore,

Two number = 29,37

Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• If 45 is subtracted from twice the greater of two numbers, it result in the other number.

• If 21 is subtract from twice the smaller number ,it resulted in the greatest number.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The numbers.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the greater number be x

And the smaller number be y

According to the 1st condition:-

If 45 is subtracted from twice the greater numbers, it result in the other number.

$\rm \implies2x - 45 = y$

$\rm \implies2x - y = 45......(i)$

According to the 2nd condition:-

If 21 is subtract from twice the smaller number ,it resulted in the greatest number.

$\rm \implies2y - 21= x$

$\rm \implies2y - x = 21$

$\rm \implies x - 2y = - 21......(ii)$

Multiplying 2 with equation (ii)

➝ 2( x - 2y = -21)

➝ 2x - 4y = - 42.....(iii)

Subtract equation (iii) from (i)

➝ 2x - y - (2x - 4y ) = 45-(-42)

➝ 2x - y - 2x + 4y = 45 + 42

➝ 3y = 87

➝ y = 29

Substituting y = 29 in equation (i)

➝ 2x - y = 45

➝ 2x - 29 = 45

➝ 2x = 45 + 29

➝ 2x = 74

➝ x = 37

We have :- x = 37 and y = 29.

$\boxed{ \rm \therefore The \: numbers \: are \: 29 \: and \: 37 }$