math word problem help

Question

average movie prices in the united states  are, in general, lower than in other countries. It would cost 78.52  to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost 74.63. How much does an average movie ticket cost in each of these countries?

 

 Japan average cost ?

 

Switzerland average cost?

Answer 1

Let x = the cost of Japanese tickets

y = the cost of Swiss tickets

 

We can create the following system of linear equations based on the info given in the problem:

 

3x + 2y = 78.52

2x + 3y = 74.63

 

If we multiply the top equation by 3, the bottom equation by 2, then we can eliminate the y-terms and wind up with:

 

5x = 86.3

x = 17.26 dollars, the avg. price of Japanese movie tickets. Now, plug this value into one of the two above equations to find y. Let's select the second one.

 

2(17.26) + 3y = 74.63

34.52 + 3y = 74.63

3y = 40.11

y = 13.37 dollars, the avg. price of Swiss movie tickets

 

 

Answer 2

J: cost of a Japan ticket

S: cost of Switzerland ticket

 

1) 3J + 2S = 78.52

2) 2J + 3S = 74.63

 

Solve for J in terms of S in equation 1:

3J = 78.52 - 2S

J = (78.52-2S)/3

 

Plug J into equation 2:

2(78.52-2S)/3 + 3S = 74.63

 

Solve for S. You will get a number value. Then plug S value back into J = (78.52-2S)/3 to get the value for J.