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.
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.
Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution
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.
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.
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.
To find the average movie ticket cost in each country, we need to set up a system of equations based on the given information. Let's assign variables to the unknowns:
Let's say the average movie ticket cost in the United States is "x" dollars.
The cost of three tickets in Japan would be 3x.
The cost of two tickets in Switzerland would be 2x.
From the given information, we can set up the following equations:
3x + 2x = $78.63 --> Equation 1 (total cost of three tickets in Japan plus two tickets in Switzerland)
2x + 3x = $74.32 --> Equation 2 (total cost of two tickets in Switzerland plus three tickets in Japan)
Now, let's solve this system of equations to find the value of "x" (average movie ticket cost in each country).
Equation 1: 3x + 2x = $78.63
Combining like terms, we get:
5x = $78.63
Dividing both sides by 5:
x = $78.63 / 5
x = $15.73
So, the average movie ticket cost in the United States is $15.73.
Now, let's substitute the value of x into Equation 1 to find the average movie ticket cost in Japan:
3x = 3 * $15.73 = $47.19
Therefore, the average movie ticket cost in Japan is $47.19.
Similarly, substituting x into Equation 2, we can find the average movie ticket cost in Switzerland:
2x = 2 * $15.73 = $31.46
Hence, the average movie ticket cost in Switzerland is $31.46.
To summarize:
- The average movie ticket cost in the United States is $15.73.
- The average movie ticket cost in Japan is $47.19.
- The average movie ticket cost in Switzerland is $31.46.