The sum of two numbers 18.The larger number is the twice the smaller number.What are they?

Question

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Answer 1

Good morning, Chloe,

Originally, I would have expressed the two numbers you are seeking as x and y. However, since we are told in the problem the following: "The larger number is twice the smaller number," i believe it safe to say that x can be used to express the one number as x and the other as 2x as this expression makes the two numbers different. With that outlined we can now solve our problem. 


X + 2X = 18   <-----The sum of two numbers is 18. 

Then, we know with certainty, that the expression 2X to be the larger number. 



Therefore: 

x + 2x = 18  

Solve:

3x = 18 

x = 6 


Now. substitute by plugging in value of x into equation:

6 + 2(6) = 18

Does this proof? Indeed, it does. 

6 + 12 =18
18=18 

Therefore, your two numbers are 6 and 12. 


Please note: Had you assigned x and y as the expressions of your two numbers, this is what would have occurred:

x + y + 18 

Solving for y would be as follows:

y = 18 -x 

Substituting you would have arrived at:

 

x + 18 - x = 18

You will notice that your x value would have cancelled leaving you with:

18 = 18 

While the above is true, you would have been no closer to determining the value of either x or y.

I hope this answer helped you and that you also have a great week. Please let me know should you have further questions or leave feedback in the comment sectio below.