Question

1f45 is subtracted from twice the greater of two numbers, it results in the other number. If 21 is subtracted from twice the smaller number, it results in the greater number. Find the numbers,​

Answer 1

Question:-

If 45 is subtracted from twice the greater of two numbers, it results in the other number. If 21 is subtracted from twice the smaller number, it results in the greater number. Find the numbers?

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Answer:-

Let the greater of two numbers be 'x' and smaller number be 'y'.

________________

Therefore,

as per question,

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

(and)

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

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Substituting value of (2) in (1), we get,

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

=4y-42-45=y

=4y-y= 42+45

=3y=87

=y=29

________________________

Substituting value of y in equation (2) , we get,

= 2(29)-21=x

= x= 58-21

= x=37

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Therefore,

x=37 and y=29

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Answer 2

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

◩ Greater number = x = 37

◩ Smaller number = y = 29

${\blue{\underline{\underline{\purple{\textsf{\textbf{Explanation : }}}}}}}$

Given that,

• 45 is subtracted from 2× the greater number it gives smaller number.
• Likewise, if 21 gets subtracted from 2× the smaller number it gives the greater number.

If we assume :

Greater number ➡ ‘x’

Smaller number ➡ ‘y’

Therefore,

A/q,

➡ 2x - 45 = y.......... (i)

➡ 2y - 21 = x...........(ii)

Using the substitution method :

• Using the substitution method we'll substitute the value of x or, y in the any equation (i) Or, (ii).

❐ Procedure :

Substituting the value of ‘x’ in equation (i) :

$\sf ⇒ \: 2x - 45 = y$

$\sf ⇒ \: 2(2y - 21) - 45 = y$

$\sf ⇒ \: 4y - 42- 45 = y$

$\sf ⇒ \: 4y - 87 = y$

$\sf ⇒ \: 4y - y = 87$

$\sf ⇒ \: 3y = 87$

$\sf ⇒ \: y = \frac{87}{3}$

$\green {\sf ⇒ \: y = 29}$

After solving we get :

➡ y = 29 (Smaller number)

• Now, to get the value of the greater number i. e., ‘x’ we'll substitute the value of ‘y’ (Smaller number) in equation (i).

Substituting the value of ‘x’ in equation (i) :

➡ 2y - 21 = x

➡ 2(29) - 21 = x

➡ x = 58 - 21

➡ x = 37 (Greater number)

${\blue{\underline{\underline{\purple{\textsf{\textbf{❃ Hence, The numbers are : }}}}}}}$

➪ Greater number $\hookrightarrow \: \sf \: x = 37$

➪ Smaller number $\hookrightarrow \: \sf \: y = 29$