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

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Discussion Overview

The discussion revolves around calculating the total amount paid for a meal costing $35 with a tip that ranges between 10% and 15%. Participants explore how to set up the equations and determine the resulting total amount, focusing on the mathematical reasoning behind the calculations.

Discussion Character

  • Mathematical reasoning
  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant states the meal cost is $35 and the tip is between 10% and 15% of that cost.
  • Another participant calculates the minimum total amount paid as $38.51 and the maximum as $40.24 based on the tip percentages.
  • A later reply reiterates the calculations and expresses a desire to understand the reasoning behind setting up the equations for the problem.
  • Another participant suggests using variables to represent the total amount and formulates inequalities to express the range of possible total amounts.
  • It is noted that the values must be discrete, leading to the interval notation of [38.51, 40.24] for the total amount paid.
  • One participant clarifies the derivation of the multipliers 1.1 and 1.15 used in the calculations.

Areas of Agreement / Disagreement

Participants generally agree on the method of calculating the total amount paid and the resulting range, but there is no consensus on the best way to set up the initial equations or the reasoning behind them.

Contextual Notes

Some participants express uncertainty about how to approach the problem initially, indicating a potential gap in understanding the setup of the equations leading to the solution.

Who May Find This Useful

Individuals interested in mathematical problem-solving, particularly in the context of calculating percentages and setting up equations for real-world scenarios.

mathdad
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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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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? :)
 
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.
 
Essentially the same thing Wilmer did, I would have let \(A\) be the total amount paid in dollars, and stated:

$$35\cdot1.1<A<35\cdot1.15$$

Or:

$$38.5<A<40.25$$

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:

$$[38.51,40.24]$$
 
Of course, 1.1 comes from adding 100 percent to 10 percent.
Also, 1.15 comes from adding 100 percent to 15 percent.
 

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