|
Question 422817: twice the sum of a number and 2is equal to three times the difference of the number and 2. find the number
Found 2 solutions by htmentor, rapaljer:
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! The 'sum of a number (call it x) and 2' means x+2
'Twice the sum' means multiply by 2: 2(x+2)
We are told this equals '3 times the difference of the number and 2' which is:
3(x-2)
Equate the two and then solve for x:
2(x+2) = 3(x-2) -> 2x + 4 = 3x - 6, or x = 10.
Check: 2*12 = 24 = 3*8
Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! Always start a word problem by identifying all the variables. By this, I mean to say "Let x = _____". In this case, there is only one variable, the unknown number, x.
Let x = the number
Then, just translate the sentence into an equation like this:
(remember that "is equal to" always means "="!)
2(x+2)=x-2
2x+4=3(x-2)
Remove the parentheses by distributive property:
2x+4=3x-6
Now, solve the equation by subtracting 2x from each side:
2x-2x+4=3x-6-2x
4=x-6
Add +6 to each side:
4+6=x-6+6
10=x
Finally, check to see if it satisfies the sentence:
The sum of the number and 2 would be 12. Twice this amount is 24. On the other side, the difference of 10 and 2 would be 8, and three times this would also be 24.
By the way, checking is always a good idea, because when I checked my original work in this problem, I MISSED IT!! I caught my error by checking it!!
Now, you really need to see my own explanation of WORD PROBLEMS on my own website! To find my website, just click on my tutor name "Rapaljer" anywhere in algebra.com. There you will find a link that takes you right to my Homepage. From my homepage, look for the link "Basic, Intermediate, and College Algebra", then select "Basic Algebra". The word problems are in Chapter 1, so look for Sections 1.09 and 1.10. Most word problems are NOT nearly as hard as they look, if you know how to set them up. This is what I tried to show you with my own "user-friendly" explanations, examples, exercises, ALL with answers too. My own students used to tell me that these are a LOT easier to understand than the traditional textbooks that were written by mathematicians for other mathematicians and publishers! What I have to offer is completely FREE!
Many of the problems in my sections are solved in detail in the corresponding "MATH IN LIVING COLOR" pages. (In fact, the fast way to find my website is to do a Google search for "Math in Living Color", and then take the link at the bottom of this page to go back to my Homepage.)
Anyway, I have a LOT of pages that may be helpful to you including my complete curriculum and a lot of solutions in COLOR to help you understand. There are also VIDEOS (on a variety of topics!) of me teaching in my classes before I retired. Best of all, it's all FREE!
Dr. R^2
Dr. Robert J. Rapalje
Seminole State College of Florida
|
|
|
| |
