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?
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]
