# Equations with variables on both sides

Discussion in 'Algebra' started by austindee, Jan 31, 2019.

1. ### austindee

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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?

austindee, Jan 31, 2019
2. ### alan whittle

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Dec 17, 2019
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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

alan whittle, Dec 17, 2019
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3. ### nycmathguy

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

nycmathguy, Jun 28, 2021

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