Answer:
total: $86.68
Step-by-step explanation:
The value of each change is found by multiplying the base amount by the percentage change. The result is rounded to the nearest cent. Here, we're applying 3 changes. In order to make sure they're rounded properly, we need to apply them in order
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<h3>discount</h3>
The discount amount is ...
discount = bill × 10% = $75.00 × 0.10 = $7.50
The discounted amount is ...
bill - discount = $75.00 -7.50 = $67.50
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<h3>tax</h3>
The tax amount is ...
tax = discounted bill × tax rate = $67.50 × 0.07 = $4.725 ≈ $4.73
The bill with tax added is ...
discounted bill + tax = $67.50 +4.73 = $72.23
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<h3>tip</h3>
The tip is apparently added to the amount after tax, so the amount of the tip is ...
tip = taxed bill × 0.20 = $72.23 × 0.20 = $14.446 ≈ $14.45
The bill with tax and tip added is ...
total bill = $72.23 +14.45 = $86.68
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<em>Additional comment</em>
At each stage, the amount can be found by using the multiplying factor (1+p), where p is the percentage change. All three factors applied gives a result of ...
75×(1-0.10)(1+0.07)(1+0.20) = 75×0.9×1.07×1.2 = 86.67
You will note this differs by a penny from the amount calculated above. That is a consequence of rounding up both the tax and the tip.
