Mia and Luke made 85 origami together. Mia made 4 pieces of origami every 3 minutes. Luke made 3 pieces of origami every 4 minutes, but Luke spent 5 minutes more than Mia. How many pieces of origami did Mia make?

Let t represent the minutes of time Mia spent making origami. Then the total output of the two was
.. t*(4/3) +(t +5)*(3/4) = 85 . . . . . . Mia's output + Luke's output = total output
.. t*(4/3 +3/4) = 85 -5*(3/4) . . . . . subtract 5*(3/4)
.. t = (325/4)/(25/12) = 39 . . . . . . divide by the coefficient of t

Mia made 39*(4/3) = 52 pieces of origami.

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A lot of folks like to solve problems involving fractions by converting them to integer problems first. You can do that here by multiplying by 12 to get
.. 16t +9(t +5) = 1020
.. 25t +45 = 1020
.. 25t = 975
.. t = 975/25 = 39
Of course, that is not necessary--especially if you have a calculator that works directly with fractions.