Question

Sum of two numbers is 83. If one exceeds the other by 15, find the numbers.

Answer 1

The two numbers are 34 and 49

The Explanation is given below -

Answer 2

Given :-

Sum of two numbers is 83

and the one number is exceed to another by 15

To Find :-

We have to find the required number

Solution :-

Let the numbers be a and b

and we have

a+b= 83

As given in the question that

b= a+15 - - - - - - eq.(i)

Now ,

$\dashrightarrow\sf\ \ a+b= 83\\ \\ \\ \dashrightarrow\sf\ \ a+a+15= 83 \ \ \ \ \ \ \ \Big[\because\ b= a+15\Big]\\ \\ \\ \dashrightarrow\sf\ 2a+15=83\\ \\ \\ \dashrightarrow\sf\ 2a= 83-15\\ \\ \\ \dashrightarrow\sf\ 2a= 68\\ \\ \\ \dashrightarrow\sf\ a= \cancel{\dfrac{68}{2}}\\ \\ \\ \dashrightarrow\underline{\boxed{\sf\ a= 34}}$

Now put the value of a in equation (i)

$\dashrightarrow\sf\ \ b= a+15\\ \\ \\ \dashrightarrow\sf\ \ b= 34+15\ \ \ \ \ \Big[\because\ b= 34\Big]\\ \\ \\ \dashrightarrow\underline{\boxed{\sf\ b= 49}}$