Question

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?

A
A+ B = 160, 4A=B
Film A. 30 min, Film B: 130 min

B. B+A= 160:48 = A
Film A 128 min, Film B, 32 min

C.AB - 160, 4A - B
Film A: 40 min, Film B: 120 min

D. 14 A+B= 160
Film A 120 min, Film B: 40 min​

Answer 1

Answer: Option a

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

Explanation:

Answer 2

Film A is 128 minutes long and Film B is 32 minutes long.

Explanation:

Here, Film A is 4 times as long as Film B i.e.,

A = 4B and

Together, the films are 160 min long i.e.,

A + B = 160

Now, name the equation

A = 4B ...(1)

A + B = 160 ...(2)

Now, put the value of A = 4B in equation (2) we get,

A + B = 160

4B + B = 160

5B = 160

B = 160 ÷ 5

B = 32

Now, put the value of B = 32 in equation (1) we get,

A = 4B

A = 4(32)

A = 128

Thus, Film A is 128 minutes long and Film B is 32 minutes long.

-TheUnknownScientist