Question

plz solve it...... ​

Answer 1

Answer :-

$\: \: \boxed{\boxed{\rm{\mapsto \: \: \: Firstly \: let's \: understand \: the \: concept \: used}}}$

Here the concept of Linear Equations in Two Variables has been used. According to this, if we take both unknown quantities as variables we can find them out using constant terms. Let's do it !!

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$\large\underline{\purple{\sf \red{\bigstar}Question:-}}$

We are two different numbers. If you add us, you get a sum of 160. If you subtract us, you get a difference of 10. Who are we?

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$\large\underline{\purple{\sf \red{\bigstar} solution:-}}$

Given,

» Sum of two numbers = 160

» Difference of two numbers = 10

• Let the bigger number be x

• Let the smaller number be y

Then, according to the question we get :-

$\large\underline{\purple{\sf \green{\bigstar}Case - I :-}}$

➣ x + y = 160

➣ x = 160 - y ... (i)

~ Case II :-

➣ x - y = 10 ... (ii)

From equation (i) and (ii), we get,

➣ 160 - y - y = 10

➣ -2y = 10 - 160

➣ -2y = -150

$\: \\ \qquad \qquad \qquad \large{\bf{\longmapsto \: \: y \: = \: \dfrac{\not{-}150}{\not{-}2} \: = \: \underline{75}}}$

➣ y = 75

$\: \\ \qquad \qquad \large{\boxed{\boxed{\sf{y \: = \: 75}}}}$

From equation (i) and the value of y, we get

➣ x = 160 - y

➣ x = 160 - 75

➣ x = 85

$\: \\ \qquad \qquad \large{\boxed{\boxed{\sf{x \: = \: 85}}}}$

$\: \\ \large{\boxed{\rm{\leadsto \: \: Thus, \: the \: larger \: number \: is \: \boxed{\bf{85}} \: and \: the \: smaller \: number \: is \: \boxed{\bf{75}}}}}$

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$\: \large{\overline{\underline{\tt{\mapsto \: \: Confused? \: Don't \: worry \: let's \: verify \: it \: :-}}}}$

For verification we need to apply the values we got into the equations we formed. Then,

:-$\large\underline{\purple{\sf \green{\bigstar}Case - Il :-:-}}$

=> x = 160 - y

=> 85 = 160 - 75

=> 85 = 85

Clearly, LHS = RHS

~ Case II :-

=> x - y = 10

=> 85 - 75 = 10

=> 10 = 10

Clearly, LHS = RHS

Here both the conditions satisfy, so our answer is correct.

Hence, Verified.

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$\; \qquad \quad \large{\underline{\sf{\underline{\leadsto \: \: Let's \: know \: more \: :-}}}}$

• Polynomials are the equations formed using constant and variable terms but the variable terms can be of many degrees.

• Linear Equations are the equations formed using constant and variable terms but the variable terms are of single degrees.

Answer 2

Answer:

solution

Given,

» Sum of two numbers = 160

» Difference of two numbers = 10

• Let the bigger number be x

• Let the smaller number be y

Then, according to the question we get :-

$\large\underline{\purple{\sf \pink{\bigstar}Case - I :-}}$

➣ x + y = 160

➣ x = 160 - y ... (i)

~ Case II :-

➣ x - y = 10 ... (ii)

From equation (i) and (ii), we get,

➣ 160 - y - y = 10

➣ -2y = 10 - 160

➣ -2y = -150

$\: \\ \qquad \qquad \qquad \small{\bf{\longmapsto \: \: y \: = \: \dfrac{\not{-}150}{\not{-}2} \: = \: \underline{75}}}$

➣ y = 75

$\: \\ \qquad \qquad \large{\boxed{\boxed{\sf{y \: = \: 75}}}}$

From equation (i) and the value of y, we get

➣ x = 160 - y

➣ x = 160 - 75

➣ x = 85

$\: \\ \qquad \qquad \small{\boxed{\boxed{\sf{x \: = \: 85}}}}$

$\: \\ \small{\{\rm{\leadsto \: \: Thus, \: the \: larger \: number \: is \: \boxed{\bf{85}} \: and \: the \: smaller \: number \: is \: \{\bf{75}}}}}$

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:-$\large\underline{\purple{\sf \orange{\bigstar}Case - Il :-:-}}$

=> x = 160 - y

=> 85 = 160 - 75

=> 85 = 85

Clearly, LHS = RHS

~ Case II :-

=> x - y = 10

=> 85 - 75 = 10

=> 10 = 10

Clearly, LHS = RHS

Here both the conditions satisfy, so our answer is correct.

Hence, Verified.