# Re: In defense....

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Posted by MathBard on October 21, 2002 at 22:59:12:

In Reply to: In defense.... posted by Subhotosh Khan on October 17, 2002 at 13:08:36:

: : : : Can you explain and show me how to do these problems?
: : : : 1. Find three consecutive odd intergers such that 7 times the sum of the first and the third is 120 less than 10 times the opposite of the second?

: : : : 2. Find three consecutive even intergers such that 6 times the sum of the first and the third is 8 less than 14 times the second?

: : : : WE are desperately seeking help. We are homeschooler and I, the mom, have been out of school for a long time! We would appreciate any help you can give us.
: : : : Thanks
: : : *****************************************
: : : odd numbers are expressed as (2*n+1) where n can be any integer.

: : : Let the first odd integer (in the series) be = 2n + 1

: : : So the next one(odd) would be 2n + 3 and the next one would be 2n + 5

: : : According to the problem"

: : : sum of first and third = (2n + 1) + (2n + 5) = 4n + 6

: : : 10*(2n + 3) - (4n + 6) = 120

: : : 20n + 30 - 4n - 6 = 120

: : : 20n - 4n = 120 - 30 + 6

: : : 16n = 96

: : : n = 6

: : : so the numbers are (2*6+1 = )13, 15, 17

: : : check:

: : : 13 + 17 = 30

: : : 10 * 15 = 150 and

: : : 150 - 30 = 120

: : : similarly you can do the second problem. Even integers are expressed as (2n). So the consecutive even integers would be (2n), (2n + 2) & (2n + 4). Carry on from there...

: : MR. Khan,
: : i recognize that your are a brilliant Mathematician, but you misread her problem.
: : You didnt notice that the problem said... the opposite of 10 time the OPPOSITE of the second.
: : here is how i did it.

: : let x equal first odd integer.
: : X+2 second odd integer
: : x+4 third

: : 7(x+x+4) is seven time the sum of first and second whis is 120 less than...
: : 7(x+x=4) + 120=
: : ten times the Opposite of the second
: : (10)(-1)(x+2)
: : all together
: : 7(x+x+4)+120=(10)(-1)(x+2)
: : simplify
: : 7(2x+4)+120=-10(x+2)
: : 14x+28+120=-10x-20
: : 14x+148=-10x-20
: : 24x=-168
: : x=-7
: : therefore
: : -7 -5 -3 are your consecutive odd ints
: ********************************
: I have never seen the term
: opposite" being used with numbers.

: You assumed it to be "additive inverse" (-ve x). But could easily assume it to be "multiplicative inverse" (1/x). However, in the later case the problem will become significantly more difficult -may be have no solution at all.

: I thought about it for a while - then decided it must have been one of those "misplaced" terms - and chose toignore it.

: I am not a mathematician - much less brilliant. I am an engineer - who likes to solve problems - problems of any kind.....

Yes, I did assume that, but the Algebra books being used today use the term "opposite" when speaking of additive inverses. This person i am sure was using one of those books.
here is one you can check or go to their website.
-Passport to Algebra and Geometry- Published by MacDougal Littell ed. by- Larson, Boswell, Kanold, & Stiff 1999 pg 105
Here is what is says:
"Two numbers that have the same absolute value but opposite signs are called opposites. For instance, -4 and 4 are opposites."

I am guessing you had Algebra 1 a wee bit before 1999? lol
MB

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