Question

A factory requires 84 machines to produce a given number of articles in 32 days. How many machines would be required to produce the same number of articles in 21 days?​

Answer 1

56 Machines

Explanation:

To solve this problem we need to use the rules of ratio and proportion.

We have:

84 Machines : 32 Days

x : 21 Days

Let x = number of machines required

84:32 can also be
`(84)/(32)`

x : 21 can also be
`(x)/(21)`

Now we can solve for x by first cross multiplying.

`(x)/(21)`=
`(84)/(32)`

32x = (84)(21)

32x = 1764

Now to find for x, we have to divide both sides by 32

`(32x)/(32)=(1764)/(32)`

x = 55.125

Now since we cannot have 1/8th of a machine we round up to 56.

We need 56 machines to produce the same number of articles in 21 days.