here is my solution

let total number of hours be y

let hourly rate be x

Total amount payed x*y=

360 ---> Hourly rate x= y/336to complete job it took 4 hours longer --> y+4

hourly rate reduced by 2 USD ---> x-2

(y+4)(x-2) = 336

plug in into above equation x= y/336

(y+4)(y/336 - 2)

336y/y - 2y+1344/y - 8 = 336

336 -2y+1344/y-8=336

-2y+1344/y= 336+8-336

-2y+1344/y =8

ok after this I got stuck and confused, where am I going what I am solving

can you please explain what have I done wrong ? I decoded the info correctly I mean expressed initially in numbers.

thanks for your help.[/quote]

If \(xy = 336\), then \(x = \frac{336}{y}\), not x = y/336.

\((y+4)(\frac{336}{y} - 2) = 336\);

\(336 - 2y + 4*\frac{336}{y} - 8 = 336\);

\(y^2 + 4y - 672 = 0\);

\(y(y + 4) = 672\)

Plug options: \(y = 24\) works.

Hope it helps.[/quote]

Bunuel - Many thanks ! Just two more question

could you show in detail how you got this \(y^2 + 4y - 672 = 0\); and another question what is the point of factoring ? \(y(y + 4) = 672\)

I remember when we see such equation\(y^2 + 4y - 672 = 0\); we need to find discriminant ? like D = B^2-4AC

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