Math
posted by Lana .
I posted this problem last night and someone answered. I followed all the steps that this person told me to do and I don't get the right answer. The right answer is suppose to be $23.54. What am I doing wrong?
For groups of four or more diners, many restaurants add a 15% gratuity and a tax of 8% to the bill. If the bill (including gratuity and tax) for four people came to $193, how much was the tip?
assume the 8% tax is added first, then the 15% tip.
So, first, add 8% to the bill amount to get a subtotal
subtotal = 193 + 0.08(193)
The same thing can be done more succinctly as follows:
subtotal = 1.08(193) $208.44
Then take 15% of that to determine the top:
tip = 0.15(subtotal)
To chain it all together:
tip = 0.15(1.08(193)) When you do this it comes to 31.26 that's not the right answer.

let the bill before taxes and tips be $x
then (1.15)(1.08)x = 193
x = 193/((1.15)(1.08))
= 155.39
After tax, bill was 155.39(1.08) = 167.83
now 15% of that is 25.17
so the tip was 25.17
check: [155.39 + .08(155.39)])1.15) = 193 
1. The School Action Society asked its members how many hours they had worked during the previous week in parttime jobs. The following data lists the number of hours spent working during the previous week.
6 6 6 4 6 6 9 8 6 3 7 6
6 7 6 6 7 6 6 8 6 7 8 4
a. From these data construct a frequency table with the included columns.
(References: example 1 and 2 page 41, end of section exercises 27, 28 page 51). Round the relative frequencies to three decimal places. (5 points)
Hours Tally Frequency
f Midpoint Relative Frequency
3  4 2.5
5  6
7  8
9  10