Sam thought of a natural number, and then he added the next natural number to it. He got the sum of 75. What was Sam’s number?

Answer 1

Call the unknown natural number x. The next one is x+1:

x + x+1 = 75

2x + 1 = 75

Solve for x.

Answer 2

Hello Selina,

The first thing you want to do to solve this problem is to assign an expression to represent each of the natural numbers.

Therefore:

x = the first number

x +1 = the second number

I am sure you know that a natural number is a number that occurs commonly and obviously in nature. As such, a natural number is a whole and non-negative number. I add this only to assist you in understanding why we can use the above expressions.

Second, we are told the sum of these two numbers is 75, right? Therefore:

x + x + 1 = 75 <-------this is simply the expressions we assigned for these numbers in equation

2x + 1 = 75 <-------Combine like terms

2x = 74 <--------Subtract one from each side of the equation.

x = 37 <--------This is the first natural number

x + 1 =

37 + 1 = 38 <--------Substitute 37 for x and solve. When we do this we arrive at next number

The two numbers are 37 and 38.

Now, we want to check our work, right? The question we want to answer is as follows:

Does 37 + 38 = 75?

Yes, it does. The solution is therefore valid and confirmed. If you need any further clarity to the solution I provide, please leave a comment directly beneath the solution I have provided you with. If you need one on one tutoring, please feel free to contact me or any tutor through the Wyzant system. Best!