Dattaprabhakar G. answered • 09/15/14
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Jessica:
Let a be the amount they spend on the meal. Add 6% tax. The tab becomes a + (0.06)a = (1.06)a. Now they tip 20% after tax (why, I do not know). So the total tab is (1.06)a +[(1.06)a](0.2) = 1.06a + 0.212 a = (1.272)a. Since they do not want to spend more than $60, set (1.272) a = 60, to give $47.16, rounded to the smaller amount in cents.
Jessica, check. 47.16 x 1.272 =59.99 (under 60). If you try 47.17 will go above 60 (not by much, but still......its the principle of the thing.)
DR. G.
Dattaprabhakar G.
Phillip R.
Thank you for your suggestion.
I wish to make two points.
1) I wanted to bring out the side-issue of when to round to the lower, the nearest or the next integer, so I had to solve the problem fully. I wonder whether or not other fellow tutors would mention rounding here.
2) On the one side I give my students complete solutions, On the other side, I make them think deeper about generalization and abstraction. I feel that when they spend less energy completing the easy tasks they are more inclined to think about the harder "thought" aspects. Each student is different. I wish I know how Jessica is. Each tutor thinks differently too.
Dattaprabhakar (Dr. G.)
P.S. Incidentally, sincere thanks for pointing out the "multiplication mishap"!
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09/15/14
Arthur D.
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Dr. G.
If you have 1.272a=60, a=60/1.272=$47.1698 which rounds to $47.17 for the meal.
6%*$47.17=$2.8302 which rounds to $2.83. $47.17+$2.83=$50 exactly.
Now add the tip of 20% which is $10 which gives $60 exactly.
If you do the tax and tip separately, you can spend $47.17 for the meal.
By the way, you gave a problem before for a student or any tutors who wanted to answer. I gave an answer using the harmonic mean if you recall. Here's one for you, or anybody else.
If an item that costs $100 is on sale for 10% off with a sales tax of 5%, does it make any difference if you take 10% off first and then add the 5% tax, or add the 5% tax first and then take the discount of 10% off ?
Think carefully. Does it matter ? To anyone ?
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09/15/14
Arthur D.
tutor
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09/15/14
Arthur D.
tutor
Dr.G.
1.272a=60, a=60/1.272=$47.1698=$47.17
0.06*$47.17=$2.8302=$2.83
$47.17+$2.83=$50
20%*$50=$10 and $10+$50=$60 exactly
I know it's only a penny but you don't have to round down unless I'm not seeing something in the problem.
You gave us a problem before and I answered it using the harmonic mean if you recall.
Here's one for students and tutors.
If a coat costing $100 is on sale for 10% off with a sales tax of 5%, does it matter if you take the discount first and then add the sales tax, or if you add the sales tax first and then take the discount ? Does it matter to anyone ?
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09/15/14
Arthur D.
tutor
Dr.G.
You can use $47.17 because 6% of $47.17=$2.83 and $2.83+$47.17=$50. 20%*$50=$10 and $50+$10=$60.
I know it's only a penny but I tried to post a problem related to this but tried twice and it would not post.
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09/15/14
Phillip R.
09/15/14