two equations

Question

four hundred tickets were sold for the RCTC play The Odd Couple. General admission tickets were $4 while student tickets were $3.  If the total ticket sales generated revenue of $1350, how much money was collected from the sale of student ticket?

Answer 1

G = number of general admission tickets

S = number of student tickets

 

  G +   S =  400  (add the numbers of each type of ticket to get the total number sold)

4G + 3S = 1350  (multiply the price per ticket for each type of ticket to get the total revenue collected)

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You can solve this one by either addition (subtraction actually) or substitution.

 

1) By addition, you must multiply the top equation by either 3 or 4 so you can subtract the bottom and have one of the variables disappear. I multiplied by 4, and solved:

 

  4G + 4S = 1600

-(4G + 3S = 1350)

 

4G + 4S = 1600

-4G -3S = -1350

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S = 250

 

Now substitute for S in either of the original equations. I picked the top equation:

 

G + 250 = 400

G= 400 - 250 = 150

 

Check by subbing the values for S and G into the bottom equation:

 

4(150) + 3(250) ?= 1350

600 + 750 = 1350 Check

 

2) By substitution, you must solve the top equation for either G or S, and substitute into the bottom equation. In this case, the addition (subtraction) method was easier, so I chose to work it out that way.