Question

(a)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?

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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★ 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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★ 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 :-

~ 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,

~ Case I :-

=> 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:

Step-by-step explanation:

$\huge{\boxed{\sf{Required \ Answer}}}$

It is said that they are 2 different numbers. So it's obvious that it will be in two variables.

Let the numbers be x and y.

So according to question:-

$\bf{x+y = 160}$

$\bf{x-y = 10}$

So there are many ways to solve the question as Elimination, substitution, Cross multiplication but wait ; which one would you choose?

Of course, the shortest and easiest one.

Let's Do!

Me chose Elimination method, the easiest one.

$\longrightarrow$ $\rm{x+y + x - y= 160 + 10}$

$\longrightarrow$ $\rm{x+y + x - y= 170}$

$\longrightarrow$ $\rm{ 2x= 170}$

$\longrightarrow$ $\rm{ x= \dfrac{170}{2}}$

$\longrightarrow$ $\sf{ x= 85}$

Now, we will place it in any equation, let me take the first one.

$\longrightarrow$ $\rm{ x + y = 160}$

$\longrightarrow$ $\rm{ 85+ y = 160}$

$\longrightarrow$ $\rm{y = 160 - 85 }$

$\longrightarrow$ $\rm{y = 75 }$

And hence the numbers are 85 and 75.

Their subtraction gives me 10.

And their addition gives me 160. Hence verified!