# In defense....

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Posted by Subhotosh Khan on October 17, 2002 at 13:08:36:

In Reply to: Re: Hints for #1 posted by MathBard on October 09, 2002 at 19:24:07:

: : : 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.....

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