What Is the Total Amount Paid for a $35 Meal with a 10-15% Tip?

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  • Thread starter mathdad
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In summary, the total amount paid for the restaurant meal must have been between $38.51 and $40.24, given that the meal cost $35 and the tip was between 10 and 15 percent. This can be represented by the inequality 35 x 1.1 < A < 35 x 1.15, where A represents the total amount paid.
  • #1
mathdad
1,283
1
A restaurant meal cost 35.00 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then the total amount paid must have been between

A. 40 & 42
B. 39 & 41
C. 38 & 40
D. 37 & 39
E. 36 & 37

My Outline:

1. The meal cost 35 dollars.

2. The tip was between 10 and 15 percent.

3. Let x = total amount paid for meal.

How do I create an equation given the above data?
 
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  • #2
10% : 35 + 3.50 = 38.50; so minimum = 38.51
15% : 35 + 5.25 = 40.25; so maximum = 40.24

Does that help...or did I confuse you? :)
 
  • #3
Wilmer said:
10% : 35 + 3.50 = 38.50; so minimum = 38.51
15% : 35 + 5.25 = 40.25; so maximum = 40.24

Does that help...or did I confuse you? :)

I understand your reply. My question is: How did you know what to do? In other words, how did you come up with the solution as you have shown? This is my main problem. I can work out the algebra but setting up the equation leading to the right answer has been my greatest struggle in terms of math today at 53 and in my younger, school days.
 
  • #4
Essentially the same thing Wilmer did, I would have let \(A\) be the total amount paid in dollars, and stated:

\(\displaystyle 35\cdot1.1<A<35\cdot1.15\)

Or:

\(\displaystyle 38.5<A<40.25\)

And since \(A\) can only be a discrete value where the quantum is the cent, or hundredth of a dollar, the solution in interval notation is:

\(\displaystyle [38.51,40.24]\)
 
  • #5
Of course, 1.1 comes from adding 100 percent to 10 percent.
Also, 1.15 comes from adding 100 percent to 15 percent.
 

FAQ: What Is the Total Amount Paid for a $35 Meal with a 10-15% Tip?

1. How do you calculate the total amount paid if the tip is between 10% and 15% of the meal cost?

The total amount paid can be calculated by adding the cost of the meal to the tip amount. This means taking the cost of the meal and multiplying it by a decimal representing the tip percentage. For example, if the meal cost $50 and the tip was 12%, the total amount paid would be $50 + ($50 x 0.12) = $56.

2. What is the significance of the tip being between 10% and 15% of the meal cost?

This range is often considered the standard amount for tipping in the service industry. It is considered a fair and appropriate amount to show appreciation for good service without being too excessive. However, the exact percentage may vary depending on the location and customs.

3. Is the tip amount included in the total amount paid or is it separate?

The tip amount is typically not included in the total amount paid and is considered a separate additional cost. This means that the total amount paid would be the sum of the meal cost and the tip amount.

4. Can the tip percentage be more than 15% or less than 10% of the meal cost?

Yes, the tip percentage can be more than 15% or less than 10% of the meal cost. The given statement only specifies that the tip falls within this range, but it can be any value within that range. It is ultimately up to the individual's discretion on how much to tip based on their satisfaction with the service.

5. How does the tip amount affect the total amount paid?

The tip amount directly affects the total amount paid by increasing the overall cost of the meal. The more you tip, the higher the total amount paid will be. However, the tip amount also shows appreciation for the service provided and can contribute to the income of the service staff.

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