Question 1209199
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Answers:
(a) <font color=red>6.5% sales tax</font>
(b) <font color=red>$726.75</font>


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Explanation for Part (a)


The discount multipliers are of the form (1-r) where 0 < r < 1
An example is r = 0.05 represents a 5% discount.
Let x be the unknown tax rate in decimal form where 0 < x < 1.
(1+x) is the sales tax multiplier.


Chaining the discounts and sales tax multipliers together will yield:
(1-0.05)*(1-0.10)*(1-0.15)*(1+x) = 0.72675(1+x)
This represents the proportion of the original price the customer pays.
<font color=green>startPrice</font>*<font color=blue>thatProportion</font> = finalPrice
<font color=green>1000</font>*<font color=blue>0.72675(1+x)</font> = 773.99


I'll let the student handle the scratch work in terms of solving that equation.
You should get this approximate solution:  x = 0.0650017
That converts to 6.50017% and rounds to <font color=red>6.5% sales tax</font> (when rounding to the nearest tenth of a percent).


Check:
1000*(1-0.05)*(1-0.10)*(1-0.15)*(1+0.065) = 773.98875 which rounds to 773.99


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Explanation for Part (b)


The quick calculation would be
1000*(1-0.05)*(1-0.10)*(1-0.15) = <font color=red>726.75</font>
Since we can multiply in any order, the order of the discounts doesn't matter.
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