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Solution to the Problem:
There are eleven prices between $10.00 and $20.00 that will yield a whole number when the
15% tip is added:
| Cost of Meal (w/o tip)
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Total Price of Meal including Tip
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| $11.30
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$12.995, which rounds to $13.00
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| $12.17
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$13.9955, which rounds to $14.00
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| $13.04
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$14.996, which rounds to $15.00
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| $13.91
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$15.9965, which rounds to $16.00
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| $14.78
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$16.997, which rounds to $17.00
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| $15.65
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$17.9975, which rounds to $18.00
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| $16.52
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$18.998, which rounds to $19.00
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| $17.39
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$19.9985, which rounds to $20.00
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| $18.26
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$20.999, which rounds to $21.00
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| $19.13
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$21.9995, which rounds to $22.00
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| $20.00
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$23.00, which rounds to $23.00
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I thought of two ways to solve this problem:
(1) Write a computer program with a for-loop to find all the values or
(2) Use algebra to solve.
Realizing that a 15% tip added to $10.00 would give $11.50,
the first possible whole number of dollars for the meal and tip would be $12.00.
Let x = cost of the meal alone
Then x + .15 x = 12.00.
Solving for x, we get x = 10.43478...
But when I checked $10.43, I got 11.9945 which rounds to $11.99.
So, I checked $10.44, and I got 12.006 which rounds to $12.01.
So, there was no solution for $12.00.
Then I checked for $13.00.
Solving x + .15x = 13.00,
I got $11.30, which gives 12.995 which rounds to $13.00.
Continue with $14.00, $15.00, ... until you get to $23.00.
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