Question

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?

Answer 1

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 $\frac{4}{3}$ of a piece per minute. Luke on the other hand can do $\frac{3}{4}$ 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 $t$ as the time Mia spent making origami. Since Luke spent 5 more minutes, we can denote his time as $t+5$.

Putting this into an equation we'll get:
$\frac{4}{3}t+ \frac{3}{4}(t+5)=85$
$\frac{4}{3}t+ \frac{3}{4}t+\frac{15}{4}=85$
$\frac{25}{12}t=81.25$
$t=39$

Therefore, Mia made pieces of origami for 39 minutes. Knowing this, we can find out the number of pieces of origami she made:
$39* \frac{4}{3} =52$

ANSWER: Mia made 52 pieces of origami.