Equations with variables on both sides

[austindee]

I am looking for the equation for this problem. I know the answer is 105 minutes. I see the answer as a ratio, but I need to set up an equation for the solution.

Selma's class is making care packages to give to victims of a natural disaster. Selma packs one box in 5 minutes and has already boxed 12 boxes. Her friend Trudy packs one box in 7 minutes and has already boxed 18 boxes. How many more minutes does each need to work in order to have packed the same number of boxes?

 

[alan whittle]

The key to this is to determine the number of boxes they will both have made. Call this N, so that Selma must make N - 12 more and Trudy N - 18.
This will take 5(N -12) minutes for Selma and 7(N-18) for Trudy.
You find N from the fact that these are equal.
Hence N = 33, and so Selma needs 21 more and Trudy 15.
As you say, this takes each of them 105 minutes

 

[nycmathguy]

The key to this is to determine the number of boxes they will both have made. Call this N, so that Selma must make N - 12 more and Trudy N - 18.
This will take 5(N -12) minutes for Selma and 7(N-18) for Trudy.
You find N from the fact that these are equal.
Hence N = 33, and so Selma needs 21 more and Trudy 15.
As you say, this takes each of them 105 minutes

We set them equal to each other and solve for N.

 

[nycmathguy]

The key to this is to determine the number of boxes they will both have made. Call this N, so that Selma must make N - 12 more and Trudy N - 18.
This will take 5(N -12) minutes for Selma and 7(N-18) for Trudy.
You find N from the fact that these are equal.
Hence N = 33, and so Selma needs 21 more and Trudy 15.
As you say, this takes each of them 105 minutes

What information 8n the statement hinted that
N - 12 and N - 18 is needed as part of the equation?