Rearranging Formulas for a and b: Common Mistakes and Correct Answers

[thomas49th]

Hi, I have to rearrange the formula to get a and b on their own. The real answers are different to mine:

p(a + b) = q (a-b) [a]

pa + pb = qa - qb

pa-qa = -qb - pb

a (p-q) = -qb - pb

a = (-qb - pb)/(p-q)

and the real answer is:

(qb + pb)/(q -p)

it's differnet to mine!

And finding rearranging to get b is

p(a + b) = q (a-b) [a]

pa + pb = qa - qb

pa-qa = -qb - pb

pb + qb = qa - pa

b(p + q) = qa - pa

b = (qa - pa)/(p + q)

and the real answer is

(pa + pa)/(q + p)

Errrrrr!

Can someone so me where i went wrong

Thanks

 

[hage567]

It's not that your answers are wrong, I think they are done properly. They just don't look exactly the same. For "a", I think that perhaps if you multiplied through by -1 after a(p-q)=-qb-pb, and arranged it based on that, your answer would turn out looking the same as the "real answer". To check, you can plug numbers into the equations and see if they turn out the same.
For "b", just change the order of p and q, it's addition anyway so it won't change anything.

 

[mjsd]

(-qb - pb)/(p-q) is equivalent to (qb + pb)/(q -p) just multiply top and bottom by -1.

for the second one you have may a misprint... check what you have typed