For ease of solving, let's first find the rate of Mia and Luke per minute. Since Mia can do 4 pieces every 3 minutes, then she can do [tex] \frac{4}{3} [/tex] of a piece per minute. Luke on the other hand can do [tex] \frac{3}{4} [/tex] of a piece per minute.
To find how many pieces they made, we first need to find the time it took for them to make the pieces. We assign [tex]t[/tex] as the time Mia spent making origami. Since Luke spent 5 more minutes, we can denote his time as [tex]t+5[/tex].
Putting this into an equation we'll get:
[tex] \frac{4}{3}t+ \frac{3}{4}(t+5)=85 [/tex]
[tex] \frac{4}{3}t+ \frac{3}{4}t+\frac{15}{4}=85 [/tex]
[tex] \frac{25}{12}t=81.25 [/tex]
[tex]t=39[/tex]
Therefore, Mia made pieces of origami for 39 minutes. Knowing this, we can find out the number of pieces of origami she made:
[tex]39* \frac{4}{3} =52[/tex]
ANSWER: Mia made 52 pieces of origami.
