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

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.

_____
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.

Answer 2

Mia made 52 pieces of origami.

Explanation:

Given :

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

Luke spent 5 minutes more than Mia.

To Find : How many pieces of origami did Mia make?

Solution :

Mia made pieces of origami in every 3 minutes. = 4

She made pieces of origami in every 1 minutes. = 4/3

Luke made pieces of origami in every 4 minutes. = 3

She made pieces of origami in every 1 minutes. = 3/4

Let total time take by Mia be t to made 85 origami together with Luke

Then time take by Luke will be (t+5) since we are given that Luke takes 5 spent 5 minutes more than Mia.

Now, Mia made pieces of origami in t minutes. =
`(4t)/(3)`

Luke made pieces of origami in t+5 minutes. =
`(3(t+5))/(4)`

Thus , The equation becomes :

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

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

`(16t+9t+45)/(12) = 85`

`(25t+45)/(12) = 85`

`25t+45 = 85*12`

`25t+45 = 1020`

`25t = 1020-45`

`25t = 975`

`t=(975)/(25)`

`t=39`

So, Mia made in 27.85 minutes =
`(4*39)/(3)` = 52

Hence ,Mia made 52 pieces of origami.