Respuesta :
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.
.. 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:
Mia made 52 pieces of origami.
Step-by-step 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. = [tex]\frac{4t}{3}[/tex]
Luke made pieces of origami in t+5 minutes. = [tex]\frac{3(t+5)}{4}[/tex]
Thus , The equation becomes :
[tex]\frac{4t}{3} +\frac{3(t+5)}{4} = 85[/tex]
[tex]\frac{4t}{3} +\frac{3t+15)}{4} = 85[/tex]
[tex]\frac{16t+9t+45}{12} = 85[/tex]
[tex]\frac{25t+45}{12} = 85[/tex]
[tex]25t+45 = 85*12[/tex]
[tex]25t+45 = 1020[/tex]
[tex]25t = 1020-45[/tex]
[tex]25t = 975[/tex]
[tex]t=\frac{975}{25}[/tex]
[tex]t=39[/tex]
So, Mia made in 27.85 minutes = [tex]\frac{4*39}{3}[/tex] = 52
Hence ,Mia made 52 pieces of origami.
