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
`(4)/(3)` of a piece per minute. Luke on the other hand can do
`(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:

`(4)/(3)t+ (3)/(4)(t+5)=85`

`(4)/(3)t+ (3)/(4)t+(15)/(4)=85`

`(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* (4)/(3) =52`

ANSWER: Mia made 52 pieces of origami.