Question 411851
A travel agency offers two Boston outings. Plan A includes hotel accommodations for three nights and two pairs of baseball tickets worth $556.40. Plan B includes hotel accommodations for five nights and four pairs of baseball tickets worth $973.

Let x represent the cost of one night's hotel accommodation and let y represent the cost of one pair of baseball tickets. Write a system of equations you could solve to find the cost of one night's hotel accommodation and one pair of baseball tickets.
Solve the system.

3x+2y=556.40......1
5x+4y=973..........2
multiply (1) by -2
-6x-4y=-1112.80
5x+4y=973
add them up
-x=-139.8
x= 139.8 one night stay.
plug value of y in (2)
139.8*5+4y=973
y = 68.50 price of ticket



The yellow pages identify two different local electrical businesses. Business A charges $50 for a service call, plus an additional $39 per hour for labor. Business B charges $32 for a service call, plus an additional $45 per hour for labor. 
Let x represent the number of hours of labor and let y represent the total charge. Write a system of equations you could solve to find the length of a service call for which both businesses charge the same amount.
Solve the system.
Which company would you use? Why?

50+39x=32+45x
6x=18
x=3 hours