Finding Tax price?

Question

How do you find what the PST and GST tax was if they only give you the tax %s and the price including taxes.

ex. GST=7%, PST=9%
price including taxes is + $19.99

7%+9%=16% TAX

19.99/1.16 (total tax) =17.23 is the price before tax.
so 19.99-17.23=2.76 this is the total amount of tax 7% and 8%.

Now how do I find out what the GST and the PST of the total tax price 2.76 are.

Answer 1

GST:
= 0.07($19.99/[1 + {0.07 + 0.09}])
= 0.07($19.99/[1 + 0.16])
= 0.07($19.99/1.16)
= 0.07($17.23)
= $1.21

PST:
= 0.09($17.23)
= $1.55

Answer: GST = $1.21, PST = $1.55

Proof:
($19.99/[1 + {0.07 + 0.09}]) + 0.07($19.99/[1 + {0.07 + 0.09}]) + 0.09($19.99/[1 + {0.07 + 0.09}]) = $19.99
($19.99/[1 + {0.16}) + 0.07($19.99/[1 + {0.16}]) + 0.09($19.99/[1 + {0.16}]) = $19.99
($19.99/1.16) + 0.07($19.99/1.16) + 0.09($19.99/1.16) = $19.99
$17.23 + 0.07($17.23) + 0.09($17.23) = $19.99
$17.23 + $1.21 + $1.55 = $19.99
$19.99 = $19.99

Answer 2

Another way of finding the GST & PST is pro-tating the $2.76:
GST = (7/16)$2.76 = $1.21
PST = (9/16)$2.76 = $1.55

Answer 3

divide by 16 and multiply by 7 for the GST tax, and/or multiply by 9 for the PST tax

Answer 4

let x = price b4 tax,
x + (7%)x + (9%)x = 19.99,
x + 0.07x + 0.09x = 19.99,
1.16x = 19.99,
x = 19.99/1.16 ~= 17.23,
GST = (7%)x ~= (0.07)(17.23) = 1.2061 ~= $1.21,
PST = (9%)x ~= (0.09)(17.23) = 1.5507 ~= $1.55.

Answer 5

let the price without tax = x
price with tax = np
then the price with tax = x + p% of x = x + [p/100]x = np
where x is the price without a tax, np is a price with tax (new price), and p is the percentage.