Alicia took a friend for a birthday dinner. The total bill for dinner was $39.74 (including tax and a tip). If Alicia paid a 23% tip, what was her bill before adding the tip?(Round your answer to the nearest cent.)
Question
Alicia took a friend for a birthday dinner. The total bill for dinner was $39.74 (including tax and a tip). If Alicia paid a 23% tip, what was her bill before adding the tip?(Round your answer to the nearest cent.)
Solution
To solve this problem, we need to find out the original cost of the dinner before the tip was added.
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We know that the total bill of $39.74 includes the original cost of the dinner and the 23% tip.
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Let's denote the original cost of the dinner as X.
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The tip is 23% of the original cost, which can be written as 0.23X.
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Therefore, the total bill is the sum of the original cost and the tip, which can be written as X + 0.23X = $39.74.
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To find the value of X, we can combine like terms on the left side of the equation to get 1.23X = $39.74.
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Finally, we can solve for X by dividing both sides of the equation by 1.23.
So, X = 32.32 (rounded to the nearest cent).
Therefore, the bill before adding the tip was $32.32.
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