SOLUTION: The sum of two numbers is thirty-three. Using x to represent the larger of the two numbers, translate "the difference between six more than twice the larger number and the sum of

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Question 191689This question is from textbook Intermediate Algebra
: The sum of two numbers is thirty-three. Using x to represent the larger of the two numbers, translate "the difference between six more than twice the larger number and the sum of the small number and three" into a variable expression. Then simplify.
(6 + 2x) - (x + 3) = 33 ? It just doesn't look right? I am having a HARD time on these kind of problems.
Thanks! This question is from textbook Intermediate Algebra

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

The reason that it doesn't "look right" is because it isn't. However, you started out on the right track.

Take it in logical pieces:

Let x represent the larger of the numbers, just like the instructions say.

You got the first bit of it right when you translated: "six more than twice the larger number" into

But then you tried to represent "the sum of the small number and three" as , when in fact that expression represents the sum of the large number and three.

The key here is the first statement in the problem. "The sum of two numbers is thirty-three." If one of the numbers is x, then the other one has to be . (Let one number be x and the other y. )

Now you can say the sum of the small number () and three is:



The second thing you did incorrectly was try to make this into an equation. The problem didn't ask for an equation, and it couldn't. The problem didn't give you anything to which the expression might equate. So, just an expression -- no equals sign.



Finally, you need to collect like terms to simplify the expression. Don't forget to use the distributive property across the second set of parentheses:





John