I m stuck on this question, i m trying to use boyles law p1xv1=p2xv2 but it doesn t make sense. however p1xv2=p2xv1 does. This is not a law?

first of all...

If we start with the ideal gas law
.. PV = nRT

and express it for 2 gases.. (or 1 gas in 2 different states)
.. P1V1 = n1*R*T1
.. P2V2 = n2*R*T2

rearranging both..
.. P1V1 / (n1T1) = R = P2V2 / (n2T2)

i.e..
.. P1V1 / (n1T1) = P2V2 / (n2T2) .... .... .<<<====== REMEMBER THIS

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next...
if we start holding different variables constant...so they cancel out..
..example..
... .if P1 = P2...
... .then P2V1 / (n1T1) = P2V2 / (n2T2)
.... and P2 cancels out leaving
.. ....V1 / (n1T1) = V2 / (n2T2)

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anyway.. holding different variables constant gives these 15 equations

zero variables held constant
(1).. [ P1V1 / (n1T1) = P2V2 / (n2T2) ]... nothing constant... not named

1 variable held constant
(2).. [ V1 / (n1T1) = V2 / (n2T2) ].. .. ...P held constant... not named
(3).. [ P1 / (n1T1) = P2 / (n2T2) ].. .. ...V held constant... not named
(4).. [ P1V1 / T1 = P2V2 / T2 ]... .. .. ...n held constant... "combined gas law"
(5).. [ P1V1 / n1 = P2V2 / n2 ].. .. ..... .T held constant... not named

2 variables held constant
(6).. [ n1T1 = n2T2 ]... .. .. ...P & V held constant... not named
(7).. [ V1/T1 = V2T2 ]... .. ....P & n held constant... "Charles law"
(8).. [ V1/n1 = V2/n2 ]... .. ...P & T held constant... "Avogadro's law"
(9).. [ P1/T1 = P2/T2 ]... .. ...V & n held constant... "Gay Lussac's law" ***
(10).. [ P1/n1 = P2/n2 ]... .. ..V & T held constant... not named
(11).. [ P1V1 = P2V2 ]... .. .. .n &T held constant... "Boyles law"

3 variables held constant
(12).. [ T1 = T2 ]... .. .. P & V & n held constant... not named
(13).. [ n1 = n2 ]... .. ...P & V & T held constant... not named
(14).. [ V1 = V2 ]... .. ...P & n & T held constant... not named
(15).. [ P1 = P2 ]... .. ...V & T & n held constant... not named

*** equation (9) is erroneously called "Gay Lussac's law" by some instructors.
.. why do I say it's erroneously called that?
.. . .(a) Gay Lussac studied gases at constant P and moles same as
.. .. .... Charles did. never constant volume !!!
... ..(b) the other gas laws at constant moles were all named, so somewhere along
.... .. ...the line some instructors found the need to name the
.. .. .. . P1/T1 = P2/T2 law... and the only "gas law scientist" without a gas law
... ... ...to his name was Mr Lussac. So they called it Gay Lussac's law in err
. . . (c) the scientist who actually studied gases at constant volume was
. ... .. . Guillaume Amonton.
. ... .. ..see the link here http://www.lookchem.com/Chempedia/Basic-Chemical/Chemical-Noun-Definition/16799.html
.. . .(d) we called that "John Doe's law" back when I took general chem.

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regardless... note the following
.. (1) all 15 of those gas laws are different variations of the ideal gas law with
... ... different variables held constant.
.. (2) some are named and some are not

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there is a better way to solve these 2 state gas law type problems then memorizing all 15 variations of the ideal gas law, for what conditions they apply, and what they're called. And praying to God you choose the right equation come test time

that process is this
.. (1) write down the general equation.. .P1V1 / (n1T1) = P2V2 / (n2T2)
.. (2) rearrange for your desired unknown
.. (3) identify anything held constant and cancel that
.. (4) plug in the data.. chug out the result... remember that T must be absolute.. K or R.. never °C nor °F

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this problem !!!

starting with
.. P1V1 / (n1T1) = P2V2 / (n2T2)

rearranging for V2
.. V2 = V1 * (P1 / P2) * (n2 / n1) * (T2 / T1)

assuming n2=n1... i.e.. the cylinder is sealed... assuming T2=T1... Temp wasn't mentioned.. assume it's constant
.. V2 = V1 * (P1 / P2)

solving
.. V2 = 800ft³ * (147 psi / 200 psi) = 588ft³

Boyle's law: P₁V₁ = P₂V₂

Proof:
By gas law, PV = nRT
R is constant. When n and T are constant: PV = constant
Hence, P₁V₁ = P₂V₂ = constant

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Initial: P₁ = 200 psi, V₁ = 800 ft³
Final: P₂ = 147 psi, V₂ = ? ft³

P₁V₁ = P₂V₂
Final volume, V₂ = V₁ × (P₁/P₂) = (800 ft³) × (200/147) = 1090 ft³ (to 3 sig. fig.)

p1*v2=p2*v1 is FALSE.
Pressure goes up when volume goes DOWN, not the other way.

You have missed a point - 'an air reservoir' is a fixed volume. Hence, 800 cf is a measure of the number of moles. The relationship between P and n is P1/n1 = P2/n2 (And this is not Boyle's Law)