Question

The difference between two number is 18. If their sum is 86, what are the numbers
With explanation please:-)

Answer 1

Answer:

Given :-

• The difference between two numbers is 18.
• Their sum is 86.

To Find :-

• What is the two numbers.

Solution :-

Let,

$\mapsto \bf First\: Number =\: x$

$\mapsto \bf Second\: Number =\: y$

According to the question :

$\bigstar$ The difference between the two numbers is 18.

So,

$\footnotesize \implies \bf \bigg\{First\: Number\bigg\} - \bigg\{Second\: Number\bigg\} =\: 18$

$\implies \sf x - y =\: 18$

$\implies \sf\bold{\purple{x =\: 18 + y\: ------\: (Equation\: No\: 1)}}$

Again,

$\bigstar$ The sum of two numbers is 86.

So,

$\footnotesize \implies \bf \bigg\{First\: Number\bigg\} + \bigg\{Second\: Number\bigg\} =\: 86$

$\implies \sf\bold{\purple{x + y =\: 86\: ------\: (Equation\: No\: 2)}}$

Now, by putting the value of equation no 1 in the equation no 2 we get :

$\implies \bf x + y =\: 86$

$\implies \sf (18 + y) + y =\: 86$

$\implies \sf 18 + y + y =\: 86$

$\implies \sf 18 + 2y =\: 86$

$\implies \sf 2y =\: 86 - 18$

$\implies \sf 2y =\: 68$

$\implies \sf y =\: \dfrac{68}{2}$

$\implies \sf\bold{\red{y =\: 34}}$

Again, by putting the value of y in the equation no 1 we get :

$\implies \sf x =\: 18 + y$

$\implies \sf x =\: 18 + 34$

$\implies \sf\bold{\red{x =\: 52}}$

$\therefore$ The two numbers are 52 and 34 .

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VERIFICATION :-

Let's verify !!

$\bigstar$ The difference between the two numbers is 18.

We have :

• x = 52
• y = 34

So,

$\footnotesize \implies \bf \bigg\{First\: Number\bigg\} - \bigg\{Second\: Number\bigg\} =\: 18$

$\implies \sf x - y =\: 18$

$\implies \sf 52 - 34 =\: 18$

$\implies \sf\bold{\blue{18 =\: 18}}$

Again,

$\bigstar$ The sum of two numbers is 86.

We have :

• x = 52
• y = 34

So,

$\footnotesize \implies \bf \bigg\{First\: Number\bigg\} + \bigg\{Second\: Number\bigg\} =\: 86$

$\implies \sf x + y =\: 86$

$\implies \sf 52 + 34 =\: 86$

$\implies \sf\bold{\green{86 =\: 86}}$

➳ L.H.S = R.H.S

➳ Hence, Verified !!

Answer 2

Step-by-step explanation:

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