In Class

Valentine's Day

Adapted from materials by Alan O'Bryan

1) Matt wants to take his girlfriend out to dinner for valentine's night, and even more so, he wants to do so in a limo!! He's called around and these are two of the choices he has left:

Limos R us charges a flat fee of $75 and then charges $40 per hour.

Limo Kings charges a flat fee of $100 and then charges $40 per hour

a) Which place is cheaper for 2 hours? 3 hours? 10 hours?

b) How many hours must Matt rent the limo for the two companies to cost the same?

c) What does this mean as a system? That is, what would the solution of this system?

d) What does this mean graphically?

e) What is it about this situation that is causing this unique case?

Record important generalizations here:

2) Think about a system of this form:

y = 3x – 7

2y = 6x – 14

a) Pick 4 values of x to test in both functions. See if they satisfy both equations, that is, see if they're solutions!!!

b) Why are your solutions coming out in the way that they are? What is it about this situation that is causing this other unique case?

Record important generalizations here