Math Is Fun Forum

glenn101

Member

Registered: 2008-04-02

Posts: 108

another polynomial identity quadratic response question

This is another question which I just don't understand.

An upholster purchased some fabric for $a. If he had brought the fabric from another supplier who charged $b per meter more he would have received b meters less for the same amount of money.

a) How many metres did he purchase, in terms of a and b?

b) If a and b, and the number of metres purchased, are natural numbers, find the possible values of a given a <100.

I don't understand how they come to the answers, for a) it ends as a quadratic formula and for b) it becomes some massive table.

Thanks,
Glenn

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John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: another polynomial identity quadratic response question

a.) e.g. $35 = 7yards at $5/yard
    but if $b=$2, then 5yards at $7/yard = $35
So, and 36 is 6 squared.
And (6-1)(6+1)=35, where 1 = half of b.
Also note that 9 squared is 81, but 7 11's is 77, which is 81 - 2^2,
and 9-2 and 9+2 timesed is 77, and 9^2 - 2^2 = 77.
If b<x, then (x + b)(x-b) = x^2 - b^2, which is how I'll solve this.
So Answer = ($a + ($b/2)^2)^0.5 + $b/2 = amount originally purchased in meters!!
The ^0.5 means square root.
One-half power is square root.
And the price per meter originally is
($a + ($b/2)^2)^0.5 - $b/2  (minus instead of plus)

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glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: another polynomial identity quadratic response question

Thank you for your response John.
Your answer seems logical and everything however, my book says otherwise:(

meters, I don't understand how they get this answer:(

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: another polynomial identity quadratic response question

Don’t listen to John – he’s just talking nonsense (he does that a lot).

Suppose the person buys x metres of cloth from the first dealer.

If he had purchased from the second dealer, he would have received x−b metres for $a.

The $ per metre in the second case would be

, and this would be b more than the original $ per metre of a⁄x. Hence

Solve that for x.

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: another polynomial identity quadratic response question

ah that makes much better sense, thanks for clearing it up jane.

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