Question

The sum of two numbers is 105 and their difference is 39. Find the numbers.
No Copy paste​

Answer 1

Given :

• Sum of two numbers = 105
• Difference of the two numbers = 39

To find :

• The numbers

Solution :

Let the two numbers be 'a' and 'b'

$\red\bigstar{\sf{According\:to\:the\:question,}}$

a + b = 105 $\longrightarrow$ eq(1)

a - b = 39 $\longrightarrow$ eq(2)

$\red\bigstar{\sf{Adding \:eq(1) \:and \:eq(2)}}$ ,

$: \implies \sf \: a + a + b - b = 105 + 39 \\ \\ \\ : \implies \sf \: 2a = 144 \\ \\ \\ : \implies \sf \: a = \frac{144}{2} \\ \\ \\ : \implies \underline{\boxed {\bf{\: a =72 }}}$

$\rule{200}{2}$

From eq(1) ,

$: \implies \sf a + b = 105 \\ \\ \\ : \implies \sf \: 72 + b = 105 \\ \\ \\ : \implies \sf \: b = 105 - 72 \\ \\ \\ : \implies \underline{ \boxed{ \bf{b = 33}}}$

∴ The Required Numbers are 72 and 33.

Answer 2

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• Sum of numbers = 105.
• Difference of numbers = 39.

$\LARGE{\bf{\underline{\underline{TO \ FIND:-}}}}$

• The two numbers.

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

So, we can use the concept of linear simultaneous equations in two variables.

Let's form the equations!

Let the two numbers be x and y.

We can form two equations:

CASE 1:

Sum = 105.

$\green \therefore \sf x+y=105 \ ---(1)$

CASE 2:

Difference = 39.

$\green \therefore \sf x-y=39 \ ---(2)$

Now we can use either methods for finding x and y.

• Substitution method

• Elimination method

• Cross-multiplication method

• Graphical method.

Lets use the elimination method.

Add (1) and (2)

$\displaystyle \sf x+y=105 \\ \underline{x-y=39}$

$\to \sf 2x=144$

$\to \sf{\red{x=72}}$

Subtract (1) and (2)

$\displaystyle \sf x+y=105 \\ \underline{x-y=39}$

$\to \sf 2y=66$

$\to \sf{\red{y=33}}$

∴ The numbers are 72 and 33.

To check (not required), I attached a graph where the two lines intersect at 72 and 33.

Regards,

Sujal Sirimilla

ex-Brainly star.