I have one more problem that I need help with. If someone can help me set up the problem I will be able to solve it for my answer. I don't know where to begin with this problem. Thank you for your help it's greatly appreciated.
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?
I 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)
Then take 15% of that to determine the top:
tip = 0.15(subtotal)
To chain it all together:
tip = 0.15(1.08(193))
To solve this problem, we can break it down into two main components: finding the bill amount before gratuity and tax, and then calculating the tip amount added to the bill.
Step 1: Find the bill amount before gratuity and tax:
Since the given total bill amount of $193 includes both the gratuity and tax, we need to first determine the bill amount before these additions. To do this, we must subtract the amounts added for gratuity and tax.
Let's assume the bill amount before gratuity and tax is "x".
Step 2: Calculate the total bill amount including gratuity and tax:
From the problem statement, we know that for groups of four or more diners, the restaurant adds a 15% gratuity and an 8% tax to the bill. So, we can express the total bill including gratuity and tax as:
x + 15% of x + 8% of x = $193
Step 3: Solve for x:
Now, we need to solve the equation to find the bill amount before gratuity and tax.
x + 0.15x + 0.08x = $193
Simplifying the equation:
1.23x = $193
Dividing both sides by 1.23:
x = $193 / 1.23
Step 4: Calculate the tip amount:
To find the tip amount, we need to calculate 15% of the bill amount before gratuity and tax which is represented by "x".
Tip = 15% of x = 0.15 * x
Step 5: Substitute the value of "x" and calculate the tip amount:
Now, substitute the value of "x" that we found in step 3 into the equation for the tip amount.
Tip = 0.15 * ($193 / 1.23)
Calculating the tip amount will provide you with the solution to the problem.
Please note: Depending on rounding rules and precision, the final answer may vary slightly.