Math Word Problem Help

Question

How would I go about solving this word problem?

 Two bicycle rental shops are competing for business. Bob’s Bicycles rents their bikes for $10.00 per day and an additional $3.00 per hour. Tony’s Ten Speed Rentals advertises a flat fee of $20 per day. 

Bob’s Bicycles: y = 3x + 10

Tony’s Ten Speed: y = 20 

a) What is the point of intersection? (Solve using a method of your choice, but not graphing)

b) What does the point of intersection represent in the context of the question? 

c) Under what conditions should you choose Bob’s Bicycles? Tony’s Ten Speed? Explain. 

Answer 1

3x + 10 = 20

3x = 10

x = 3 1/3 hours when Bob's and Tony's charge the same: $20

point of intersection = (x,y) = (3 1/3, 20)

for more than 3 1/3 hours Tony charges less

for less than 3 1/3 hours Bob charges less