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June 18th, 2012, 11:35 PM  #1 
Newbie Joined: Jun 2012 Posts: 20 Thanks: 0  Translating Equations
Translate into an equation and solve. (Use n to represent the smaller number.) The sum of two numbers is nine. Seven less than three times the smaller is equal to the larger. Find the numbers. :(smaller number) :(larger number) Struggling a little bit with this. So I got x+x=9 3x7=? Completely lost, its also asking me to find the smaller and larger number... Help 
June 18th, 2012, 11:41 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Translating Equations
If we use n to represent the smaller number and m to represent the larger, then from the given information, we have: (1) We can rewrite the second equation as: (2) Now, adding (1) and (2), we find: Solving (1) for m we then find: 
June 19th, 2012, 12:05 AM  #3 
Newbie Joined: Jun 2012 Posts: 20 Thanks: 0  Re: Translating Equations
Thanks Mark, you explained it way better than my book did. I wrote down your example to study for my test.

June 19th, 2012, 12:13 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Translating Equations
For most students, the difficulty is translating the given statements into equations. Once you have the correct equations, then its usually just a matter of elimination or substitution to find the solution.

June 19th, 2012, 12:14 AM  #5  
Senior Member Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14  Re: Translating Equations Quote:
 
June 19th, 2012, 12:25 AM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Translating Equations
It is easier to give an explanation for one problem, then for an entire set of exercises. 
June 19th, 2012, 07:17 PM  #7 
Newbie Joined: Jun 2012 Posts: 20 Thanks: 0  Re: Translating Equations
Getting the hang of translating, although I'm stuck on this problem: Find two consecutive even integers such that six times the first integer equals three times the second integer. Find the smallest integer and largest integer. Equation I came up with is 6x= 3(x+2) 6x= 3x+6 3x= 6 x=2 So now I substituted my 2 back 2+2= 4 2+4= 6 Now my smallest integer is 2. My largest is 6. But when I enter this in my homework it says I'm wrong; am I missing something? 
June 19th, 2012, 07:19 PM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Translating Equations
You set up the equation correctly and solved correctly. x represents the smaller, which is 2 and x + 2 is the larger which is 4. 

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