for every part produced by a factory, there are 5 ounces of scrap aluminum that can be recycled. there are 16 ounces in 1 pound and 2,000 pounds in 1 ton. how many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling

The rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: [tex]x=\frac{cxb}{a}[/tex]

How many parts are produced by the factory?

The direct rule of three is the rule applied in this case where there is a change of units.

To perform in this case the conversion of units, you must first know that:

there are 16 ounces in 1 pound.
there are 2,000 pounds in 1 ton.

You want to know how many parts must the factory produce so that there is 1 ton of scrap aluminum for recycling. So, first, in 1 ton there are 2,000 pounds.

Then, you can apply the following rule of three: if there are 16 ounces in 1 pound, how many ounces are there in 2,000 pounds?

1 pound ⇒ 16 ounces

2,000 pounds ⇒ x

So: [tex]x=\frac{2000 poundsx16 ounces}{1 pound}[/tex]

Solving:

x= 32,000 ounces

This is, there are 32,000 ounces in 1 ton.

Then, for every part produced by a factory, there are 5 ounces of scrap aluminum that can be recycled. So, you can apply the following rule of three: If for every part produced by a factory there are 5 ounces of scrap aluminum that can be recycled, in how many parts produced by the factory are there 32,000 ounces of scrap aluminum that can be recycled?

[tex]number of parts=\frac{32,000 ouncesx1 part}{5 ounces}[/tex]

number of parts= 6,400 parts

In summary, 6,400 parts the factory must produce so that there is 1 ton of scrap aluminum for recycling.

Learn more about change of units with this example:

brainly.com/question/12482948?referrer=searchResults

#SPJ2