Math problem

Question

Average movie prices in the US are, in general, lower then in other countries. It would cost $77.57 to buy three tickets in Japan plus two tickets in Switzerland. 3 tickets in Switzerland plus 2 tickets in Japan would cause $73.35. How much dies an average movie ticket cost in each of those countries?

 

Assign two variables, x & y. Set up a system of two equations and solve.

Hint: Both of the equations will be "cost equations".

Answer 1

Use a system of cost equations and substitution method to solve.

Let: J = Average cost of ticket in Japan, S = Average cost of ticket in Switzerland 

 

So,

a.) 3J + 2S = 77.57   (multiply eq. by 2 in next step)

b.) 2J + 3S = 73.35   (multiply eq. by 3 in next step) 

 

aa.) 2 (3J + 2S) = 77.57 (2)   ===>   6J + 4S = 155.14

bb.) 3 (2J + 3S) = 73.35 (3)   ===>   6J + 9S = 220.05  

 

Now, subtract bb.) - aa.)

  6J + 9S = 220.05

- 6J + 4S = 155.14
 _______________   

          5S = 64.91

            S = $12.98

 

Now, substitute value of S into eq. a.)  3J + 2(12.98) = 77.57 

3J + 25.96 = 77.57

3J = 77.57 - 25.96 = 51.61 

J = 51.61 / 3  ==>  J = $17.20