If the tip was more than 10% but less than 15% of the cost of the meal, then the total amount paid

[mathdad]

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?

 

[Wilmer]

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? :)

 

[mathdad]

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.

 

[MarkFL]

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:

\(\displaystyle [38.51,40.24]\)

 

[mathdad]

Of course, 1.1 comes from adding 100 percent to 10 percent.
Also, 1.15 comes from adding 100 percent to 15 percent.