Question

Sum of two numbers is 95. If one exceeds the other by 15, find the numbers.

Answer 1

Hint: We will first assume a number and find another one according to that. Now, we will sum them both to get 95 and thus get the required value.

Complete step-by-step answer:
Let us assume that one of the number is x.
Now, since it is given that the other exceed by 15, so the other number is ‘x + 15’.
Since, sum of both of them is given to be 95.
So, we have: x + x + 15 = 95
Clubbing both of the x’s pn the left hand side in the above expression to obtain the following expression:-
$ \Rightarrow $2x + 15 = 95
Taking the 15 from addition in the left hand side to subtraction in the right hand side in the above expression to obtain the following expression:-
$ \Rightarrow $2x = 95 – 15
Doing the mentioned calculations on the right hand side, we will then obtain the following:-
$ \Rightarrow $2x = 80
Taking the 2 from multiplication in the left hand side to division in the right hand side to obtain the following expression:-
$ \Rightarrow $x = 40
Now, since the one number is 15, so the other number is 40 + 15 = 55.

Hence, the two numbers are 40 and 55.

Note:
The students must note that, here, we have 1 variable x which eventually gives us one solution and we find other number using that only.
There is an alternate way to do the same. We can call it alternate way, it is just that we will form two equations here.
Let the one number be ‘x’ and let the other number be ‘y’.
Now, since we are given that one number exceeds 15 the other number, so y = x + 15.
Now, their sum is 95, so, we have: x + y = 95
Putting the value of y from above, we have:- x + x + 15 = 95
Clubbing both of the x’s on the left hand side in the above expression to obtain the following expression:-
$ \Rightarrow $2x + 15 = 95
Taking the 15 from addition in the left hand side to subtraction in the right hand side in the above expression to obtain the following expression:-
$ \Rightarrow $2x = 95 – 15
Doing the mentioned calculations on the right hand side, we will then obtain the following:-
$ \Rightarrow $2x = 80
Taking the 2 from multiplication in the left hand side to division in the right hand side to obtain the following expression:-
$ \Rightarrow $x = 40
Now, put this in y = 40 + 15 = 55
Hence, the other number is 55.