The sum of two numbers is 31. The difference between the same two numbers is 21. What are the two numbers?

Answer 1

Hello Zemarion,

So, let's solve the problem this way, fair enough?

First, allow x and y represent the two numbers in the problem, okay?

Second, just read the problem: "The sum of two numbers is 31." And, the "Difference between the same two numbers is 21," okay?

Thirds, let's write two equations to represent the words in the problem:

First x + y = 31 "the sum of two numbers is 31."

Second x - y = 21 "the differnce between the exact numbers is 21."

Notice the y variable cancels out, correct? Therefore:

x + y = 31

x - y = 21

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2x = 52

x = 26 <------The first number

Now, we can substitute 26 for the value of x, correct?

x + y = 31

26 + y = 31

y = 5 <------The second number

Finally, we always check our work, correct>

Is the sum of 26 plus 5 equal to 31? Yes.

Is the difference of 26 and 5 equal to 21? Yes.

The values and answer check out and the solution is therefore valid. I hope this assists you, and should you wish to leave feedback, or present futher clarity, or have additional questions, please provide that information via a comment directly underneath this solution. If you need one on one tutoring, please feel free to contace me or any other tutor. Have a Happy Thanksgiving break! Best!