## Translating word problems

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
Rawshark
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Joined: Tue Nov 02, 2010 8:46 pm
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### Translating word problems

I read the article on this site on the topic of translating word problems, as well as the part of my math book on it, but I've got a few problems that I just can't seem to translate. Could anyone help, please?

1st problem:
The sum of two numbers is 42. One number plus 2 times the other number is 57. What are the two numbers?

My math teacher helped me translate it, and he said that it would be written as 57=(42-y)-2y, but I think he made a mistake translating it or I did in solving it, because I keep coming up with y = -5 and the answer key said it should be y = 15

Here's how I tried to do it:
57 = (42-y) - 2y
57 = 42 - 3y
15 = 3y
-5 = y

Does anybody know what went wrong here?

And if you're not too sick of me by now, I have another word problem that I really can't translate at all.

2nd problem:
The difference between two numbers is -38. Two times the smaller number minus five times the larger number is -217. What are the two numbers?

Any help would be greatly appreciated, and sorry for asking you guys to help me with all this at once. ^^;

stapel_eliz
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Joined: Mon Dec 08, 2008 4:22 pm
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1st problem: The sum of two numbers is 42. One number plus 2 times the other number is 57. What are the two numbers?

My math teacher helped me translate it, and he said that it would be written as 57=(42-y)-2y....
If you're working with "plus", why is there a "minus" sign on the right-hand side of the equation?
2nd problem: The difference between two numbers is -38. Two times the smaller number minus five times the larger number is -217. What are the two numbers?
Use the same translation technique as you used for the other "number" exercise:

. . . . .one number: x
. . . . .other number: y
. . . . .difference: x - y = -38

...so the "other number" may be stated as:

. . . . .x + 38 = y

Since x - y was negative, then y is the "larger" number, in addition to being the "other" number. Translate "2 times (smaller) minus 5 times (larger) is -217" into an equation. Solve for x. Back-solve for y.

Rawshark
Posts: 2
Joined: Tue Nov 02, 2010 8:46 pm
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### Re: Translating word problems

Wow! Thank you so much! I think I get it now.
If you're working with "plus", why is there a "minus" sign on the right-hand side of the equation?
Oh, jeez, I can't believe I missed that.

Thank you again! You helped me a lot.