two workers can make two chairs in two days how many chairs can eight workers make in twenty days

Question

no additional details

Answer 1

hi Marlecia,

This is a problem in rates and I believe there is a little twist that can make this problem difficult. Let's think about it as "how many chairs can a pair of workers make per day?". We know that a pair of workers can make 2 chairs every 2 days, which is a rate of 1 chair per day per pair of workers.

If we multiply this rate by 20, we have that a pair of workers can make 20 chairs in 20 days.

The question is how many chairs can 8 workers make in 20 days. In other words, how many chairs can 4 pairs of workers make in 20 days. And we know that each pair of workers can make 20 chairs in 20 days. So, multiplying this rate by 4 gives us 80 chairs in 20 days.

 

Answer 2

8 workers make 80 chairs in 20 days

if 2 workers make 2 chairs in 2 days

workers and chairs vary directly

chairs and days vary directly

c varies jointly with w and d, k=constant of proportionality = 1/2=.5

c = kwd

2 = k2(2) = 4k

k = 2/4 = 1/2

c = .5wd

c = .5(8)20 = 80 chairs in 20 days with 8 workers

Answer 3

My Apologies Marlecia,

I posted my first reply around 2:30AM - 3:00AM when i should have just gone to sleep.

Jason is right. I plugged the number 10  in where I should have put 20.

Below is my adjusted answer:

 

When you have a problem that gives you an equation like the one above:

two workers can make two chairs in two days

 

It is really saying  "2workers x 2days = 2chairs" or "2w x 2d=2c"

Break it down into smaller units. Every 2 days you will have 2 chairs.

How many chairs will you have in 20 days from those 2 workers? The answer is 20 chairs.

Add those smaller units together until you have 8 workers:

2w x 20d = 20chairs

2w x 20d = 20chairs               

2w x 20d = 20chairs

2w x 20d = 20chairs

8 workers     =     80 chairs

 

Well, Marlecia, I hope this helps.

George L  ::::

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P.S. Again, I am sorry if i caused you any confusion.