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June 18th, 2012, 11:35 PM   #1
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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 3x-7=?

Completely lost, its also asking me to find the smaller and larger number... Help
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June 18th, 2012, 11:41 PM   #2
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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:

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June 19th, 2012, 12:05 AM   #3
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Re: Translating Equations

Thanks Mark, you explained it way better than my book did. I wrote down your example to study for my test.
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June 19th, 2012, 12:13 AM   #4
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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.
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June 19th, 2012, 12:14 AM   #5
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Re: Translating Equations

Quote:
Originally Posted by IDoNotLikeMath
Thanks Mark, you explained it way better than my book did. I wrote down your example to study for my test.
Mark and someone outta there is always the book
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June 19th, 2012, 12:25 AM   #6
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Re: Translating Equations

It is easier to give an explanation for one problem, then for an entire set of exercises.
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June 19th, 2012, 07:17 PM   #7
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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?
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June 19th, 2012, 07:19 PM   #8
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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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