Question

if 45 is subtracted from twice the greater of two numbers it results in the another number. If 21 is subtracted from twice the smaller number it results in greater number. find the numbers.

Answer 1

Let, greater no.= x
Smaller no. = y
2x-45=y => 2x-y =45
And 2y-21= x => -x+2y = 21

As, coefficient of y is coefficient of x in other equation,
We need to first subtract then add them
Equation 1 - Equation 2 = 3x-3y =24
Equation 1 + equation 2 = x+y= 66
now by addition - substraction method,
3x-3y = 24
3x+3y = 198 (addition)
6x = 222 => x = 37
Now, 37+y=66 => y = 66-37
=> y = 29
The greater no. Is 37 while smaller is 29

Answer 2

Answer:

Step-by-step explanation:

Given :-

If 45 is subtracted from twice the greater of two numbers it results in the another number.

If 21 is subtracted from twice the smaller number it results in greater number.

To Find :-

The numbers.

Solution :-

Let the greater number be x

And the smaller number be y.

According to Question.

1st Equation

⇒ 25x – 45 = y  

⇒ 2x – y = 45 ……….(i)  

2nd Equation

⇒ 2y - 21 = x

⇒ –x +2y = 21 ………(ii)  

On multiplying (i) by 2,

4x - 2y = 90 ………..(iii)

 

On adding (ii) and (iii),

⇒ 3x = (90 + 21) = 111  

⇒ x = 111/3

⇒ x = 37  

Putting x value in eq (i)

⇒ 2x – y = 45

⇒ 2 × 37 - y = 45  

⇒ 74 - y = 45  

⇒ y = (74 - 45) = 29  

⇒ y = 29

Hence, the greater number is 37 and the smaller number is 29.