Question

Average movie prices in the United States are, in general, lower than in other countries. It would cost $78.63 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $74.32. How much does qn average movie ticket cost in each of these countries.

Answer 1

Let's assume the cost of an average movie ticket in the United States is x dollars.

Using this assumption, we can set up two equations to represent the given information:

3y + 2z = 78.63

3z + 2y = 74.32

where y represents the cost of an average movie ticket in Japan and z represents the cost of an average movie ticket in Switzerland.

Simplifying the equations, we get:

3y + 2z = 78.63

2y + 3z = 74.32

We can solve for y in the first equation:

3y + 2z = 78.63

3y = 78.63 - 2z

y = (78.63 - 2z)/3

We can then substitute this expression for y into the second equation:

2((78.63 - 2z)/3) + 3z = 74.32

52.42 - (4/3)z + 3z = 74.32

(5/3)z = 21.9

z = 13.14

Substituting this value back into the expression for y:

y = (78.63 - 2(13.14))/3 = 17.45

Therefore, the average movie ticket prices in Japan, Switzerland, and the United States are approximately $17.45, $13.14, and x, respectively.

Answer 2

Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution

Answer 3

To make 80 liters of a 30% acid solution, you would need:

- 24 liters of pure acid (since 30% of 80 is 24)
- 56 liters of a neutral solution to mix with the pure acid to make a total of 80 liters

So you would mix 24 liters of acid with 56 liters of neutral solution to make 80 liters of a 30% acid solution.

Answer 4

Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60% solution. How many liters of each does he need to make the need 80 liters of 30% acid solution.

Answer 5

Let x be the number of liters of the 20% solution that Gabe needs and y be the number of liters of the 60% solution that he needs.

To make 80 liters of a 30% solution, the amount of acid in the mixture must be:

0.3(80) = 24 liters

We know that we need a total of 80 liters of solution, so:

x + y = 80

We also know that the amount of acid in the 20% solution is:

0.2x

Similarly, the amount of acid in the 60% solution is:

0.6y

The total amount of acid in the final mixture is 24 liters, so:

0.2x + 0.6y = 24

Now we have two equations:

x + y = 80

0.2x + 0.6y = 24

We can use algebra to solve for x and y. Here's one way to do it:

1. Multiply the first equation by 0.2 to get:

0.2x + 0.2y = 16

2. Subtract the above equation from the second equation to eliminate x:

0.6y - 0.2x - 0.2y = 24 - 16

0.4y = 8

y = 20

3. Substitute y = 20 into the first equation to solve for x:

x + 20 = 80

x = 60

So Gabe needs 60 liters of the 20% solution and 20 liters of the 60% solution to make 80 liters of a 30% solution.