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if a-p-b,and if  ap=2x-9,ab=32,andpb=1.5x=6 then find pb

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patriciabmcca... | High School Teacher | eNoter

Posted January 7, 2013 at 6:46 PM via web

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if a-p-b,and if  ap=2x-9,ab=32,andpb=1.5x=6 then find pb

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 9, 2013 at 5:07 PM (Answer #1)

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The information provided by the problem is incomplete since, `a-p-b`  is not given, hence, considering only the given conditions, you may evaluate `x`  such that:

`ap=2x-9 => p = (2x-9)/a`

`ab=32 => b = 32/a`

`pb=1.5x + 6`

Substituting `32/a`  for `b`  and `(2x-9)/a`  for `p`  yields:

`(32/a)*(2x-9)/a = 1.5x + 6`

`32(2x - 9) = a^2(1.5x + 6)`

`64x - 288 = 1.5xa^2 + 6a^2`

Isolating the terms that contain `x`  to the left side yields:

`64x - 1.5xa^2 = 288 + 6a^2`

You need to factor out x such that:

`x(64 - 1.5a^2) = 288 + 6a^2 => x = (288 + 6a^2)/(64 - 1.5a^2)`

Hence, evaluating x you may find the products `ap`  and `pb` .

Notice that the evaluation of `x` , under the given conditions, depends on the variable a such that `x = (288 + 6a^2)/(64 - 1.5a^2).`

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