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02 Jun 2020, 05:46
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Original
cost: \(\frac{P+20}{1.25}\) Tip: \(\frac{0.18P+3.6}{1.25}\)
cost: \(\frac{P+20}{1.25}\) Tip: \(\frac{0.18P+3.6}{1.25}\)
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Difficulty:
55%
(hard)
Question Stats:
68% (03:01) correct
32%
(03:11)
wrong
based on 1679
sessions
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Maria and her companion had a $20 gift certificate to a restaurant. They applied the certificate to the cost of their meal but left an 18% tip based on the original cost of the meal. They also paid 7% sales tax that was applied to the original cost of the meal.
Let P denote the total amount Maria and her companion paid, in dollars, after the gift certificate had been applied to the bill. Select Original cost for the expression that represents the original cost of the meal, and select Tip for the expression that represents the tip they paid, in dollars. Make only two selections, one in each column.
Let P denote the total amount Maria and her companion paid, in dollars, after the gift certificate had been applied to the bill. Select Original cost for the expression that represents the original cost of the meal, and select Tip for the expression that represents the tip they paid, in dollars. Make only two selections, one in each column.
|
Original cost |
Tip | |
| \(\frac{P-20}{1.25}\) | ||
| \(\frac{P+20}{1.25}\) | ||
| \(\frac{0.25P+5}{1.25}\) | ||
| \(0.18*(\frac{P-20}{1.25})\) | ||
| \(\frac{0.18P+3.6}{1.25}\) |
ShowHide Answer
Official Answer
Original
cost: \(\frac{P+20}{1.25}\) Tip: \(\frac{0.18P+3.6}{1.25}\)
cost: \(\frac{P+20}{1.25}\) Tip: \(\frac{0.18P+3.6}{1.25}\)
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02 Jun 2020, 06:09
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Let original cost be x
So here per the question
x-20(gift card)+.18x(Tip based on original cost)+.07x(Sales tax applied on original cost)= P
1.25x-20=P
x= (P+20)/1.25
And now the Tip is 0.18x= 0.18(P+20)/1.25
(0.18P+3.6)/1.25
Posted from my mobile device
So here per the question
x-20(gift card)+.18x(Tip based on original cost)+.07x(Sales tax applied on original cost)= P
1.25x-20=P
x= (P+20)/1.25
And now the Tip is 0.18x= 0.18(P+20)/1.25
(0.18P+3.6)/1.25
Posted from my mobile device
14 Apr 2021, 06:15
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Official Explanation
RO1
The amount Maria and her companion paid for their meal (P) is equal to the Original cost of the meal (which can be denoted C) plus the tip (0.18C) plus the tax (0.07C) minus the gift certificate (20). Thus, P = C + 0.18C + 0.07C − 20 = 1.25C − 20P = C + 0.18C + 0.07C − 20 = 1.25C − 20. Adding 20 to both sides of the equation yields P + 20 = 1.25C. Dividing both sides of the equation by 1.25 yields \(\frac{P+20}{1.25} = C\).
The correct answer is \(\frac{P+20}{1.25}\)
RO2
The Tip left by Maria and her companion is 18% of the Original cost of their meal, or 0.18C. Using the expression for C from the analysis of RO1, the Tip equals 0.18 \((\frac{P+20}{1.25})\). Multiplying both terms in the numerator by 0.18 yields the expression \(\frac{0.18P+3.6}{1.25}\)
The correct answer is \(\frac{0.18P+3.6}{1.25}\)
RO1
The amount Maria and her companion paid for their meal (P) is equal to the Original cost of the meal (which can be denoted C) plus the tip (0.18C) plus the tax (0.07C) minus the gift certificate (20). Thus, P = C + 0.18C + 0.07C − 20 = 1.25C − 20P = C + 0.18C + 0.07C − 20 = 1.25C − 20. Adding 20 to both sides of the equation yields P + 20 = 1.25C. Dividing both sides of the equation by 1.25 yields \(\frac{P+20}{1.25} = C\).
The correct answer is \(\frac{P+20}{1.25}\)
RO2
The Tip left by Maria and her companion is 18% of the Original cost of their meal, or 0.18C. Using the expression for C from the analysis of RO1, the Tip equals 0.18 \((\frac{P+20}{1.25})\). Multiplying both terms in the numerator by 0.18 yields the expression \(\frac{0.18P+3.6}{1.25}\)
The correct answer is \(\frac{0.18P+3.6}{1.25}\)
