Let's do this in two steps:

(1) calculate sale price:

15% off of $52. So, the sale price is 85% of the original price, or .85(52).

Now, we could actually calculate it the traditional way, or we could just kind of "figure it out".

10% of $52 is 5.20. Half of that would be 5%, so another 5% is 2.60. So, 15% off is 5.20 + 2.60 = 7.80.

52.00 - 7.80 = 44.20.

(2) calculate the tax:

5% tax, so we owe an extra 5% of 44.20. 10% of 44.20 woudl be 4.42, so 5% is half of that, which is 2.21.

(3) find the final cost, including tax:

44.20 + 2.21 = 46.41.

* * *

If I actually saw the answer choices, I may have decided to backsolve/reason it out instead - it would largely depend on how spread out they are.

anoher way to do it is..
price given 52
there are 2 factors which are affecting the price, sale tax & the discount.
both the percentages are given, so simply apply them together..

85*105*52/100*100
simplyfi it & thats your answer..

Whenever the tax, discount & all those parameters which affect the price of items are given, apply them together. This will ease out your calculations.
regards
Ritz