Write and solve a system of equations to solve the problem.
At a film festival, Film A is 4 times as long as Film B. Together, the films are 160 min long. How long is each film?
Write and solve a system of equations to solve the problem.
At a film festival, Film A is 4 times as long as Film B. Together, the films are 160 min long. How long is each film?
AB = 160; 4A = B
Film A: 40 min, Film B: 120 min
40 * 4 =160
120+40=160
A = 4 B
A + B = 160
_____________
A + B = 160
4 B + B = 160
5 B = 160 Divide both sides by 5
B = 160 / 5 = 32 min
A = 4 B = 4 * 32 = 128 min
Let's denote the length of Film B as "x" minutes.
According to the problem, Film A is 4 times as long as Film B. Therefore, the length of Film A is 4x minutes.
Together, the films are 160 minutes. So, the equation representing the total length of the films can be written as:
x + 4x = 160
Combine like terms:
5x = 160
To solve for "x", divide both sides of the equation by 5:
x = 160/5
x = 32
Therefore, Film B is 32 minutes long.
To find the length of Film A, substitute the value of x into the equation:
4x = 4(32) = 128
Therefore, Film A is 128 minutes long.
So, Film A is 128 minutes long, and Film B is 32 minutes long.
To solve this problem, we can set up a system of equations. Let's define the variables:
Let's say that the length of Film B is represented by the variable 'B', and the length of Film A is represented by the variable 'A'.
Given that Film A is 4 times as long as Film B, we can express this as:
A = 4B
We also know that the total length of both films is 160 minutes. We can express this as:
A + B = 160
Now we have our system of equations:
A = 4B
A + B = 160
To solve this system of equations, we can use the method of substitution or elimination. Let's use substitution.
First, substitute the value of A from the first equation into the second equation:
4B + B = 160
Combine like terms:
5B = 160
Next, solve for B by dividing both sides of the equation by 5:
B = 32
Now that we know the length of Film B is 32 minutes, we can substitute this value back into the first equation to find the length of Film A:
A = 4(32)
A = 128
Therefore, Film B is 32 minutes long, and Film A is 128 minutes long.