SOLUTION: The sum of two numbers is 43. The second is 1 more than 2 times the first. What are the two numbers?

Question 44837: The sum of two numbers is 43. The second is 1 more than 2 times the first. What are the two numbers?
Answer by Chris435435(8) (Show Source): You can put this solution on YOUR website!
When working with algebra word problems, I always look at what they ask for. The question is asking us to find two numbers. Let's represent these two numbers by x and y where x is the larger number and y is the smaller number.
The sum of the two numbers x and y is 43... that is:

There is more information in the problem though. We also know that the larger number x is "1 more than 2 times the smaller number". So we should multiply the smaller by 2 and add 1 to it right? By doing this, we get x:

This is a system of equations which must be solved for. Hopefully, you know how to solve a system of equations. However, here is a worked out solution:

Plug y into one of the equations and you'll get x:

Therefore, our two numbers are 29 and 14 which add up to 43 and satisfy the condition that the larger number is twice the smaller plus 1.
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Keep in mind that this isn't the only way to solve the problem. When it comes to word problems, you have some freedom in solving the problem the way you want. Of course, keep it logical and correct. For instance, notice that I defined my variables so that x was the larger number and y was the smaller number. However, it you wanted to, you could have defined it so that x was the smaller number and y was the larger. Of course, our equations would change. Since y is the larger number, then y must be twice the smaller plus 1. That is:

Also, the other condition must be satisfied, that is,
.
So you see, it's all in how you define your variables. That is one of the most important steps in solving the problem.
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