SOLUTION: Lucky's Shop Mart is a local business that sells a variety of items. One of those is a computer with a sticker price of $1000.
Monthly members get an automatic 30% discount on eve
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Question 1209196: Lucky's Shop Mart is a local business that sells a variety of items. One of those is a computer with a sticker price of $1000.
Monthly members get an automatic 30% discount on everything in the store. During the months of August and September, a back-to-school 25% discount is applied to computers only. The discounts stack.
The state sales tax is 7%. County sales tax is a separate 2.5%.
Fred is a monthly member who uses a 10% discount coupon to buy a computer on September 3rd.
How much does Fred pay for the computer after including all three discounts and the two types of sales tax? Round to the nearest cent.
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
Answer: $517.39
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Quick calculation in one line
1000*(1-0.30)*(1-0.25)*(1-0.10)*(1+0.07+0.025) = 517.3875 which rounds to $517.39
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Explanation
For now let's focus on the (1-0.30)*(1-0.25)*(1-0.10) portion.
Each factor is of the form (1-r) where 0 < r < 1.
Each factor represents a different discount multiplier.
For instance, the 30% discount is 1-r = 1-0.30
We could simplify this to 0.70, but I find it's better to leave it unevaluated so we can spot the 0.30 quickly.
The (1+0.07+0.025) portion represents the overall tax multiplier when combining the two individual tax rates.
This expression simplifies to 1.095 to represent a combined tax rate of 9.50%.
Consider an item worth $100. The 7% and 2.50% tax rates will yield $7 and $2.50 of tax respectively. So that's 7+2.50 = 9.50 dollars of total tax. Then 9.50/100 = 9.50%.
We can think of it like saying 7%+2.50% = 9.50%; normally percentages do not add like this but with tax rates it's an exception. This is because each tax rate applies to the same starting cost.
The order of the multipliers does not matter.
This means we can apply discounts first and tax later, or tax first and discount later, or do some other mixed combo. We'll arrive at the same final answer regardless of order.
Note: This final result does not include the price of the monthly membership.
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