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4.7a: Percents as proportions and applications - translate and solve
Percent proportions can be translated as long as you remember a little formula.
This formula is simply written as "is" over "of"
otherwise known as part over whole equals your percent over 100.
We are going to look at translating word sentences into proportions
and then solving them.
If we look at the first example, it says what percent of 25 is 16.
This means we need to identify each of the parts.
We have the "off" and we have the "is."
The "is" is the part and it goes in the numerator.
The "of" is the whole and therefore goes in the denominator.
Remember that this is equal to the other fraction
which is percent which we will show as X since we do know what it is over 100.
We now need to solve the proportion.
Remember an easy way to solve a proportion is to clear the fractions.
You can clear fractions by multiplying by its products or in this case 100 x 25.
You may then reduce which eliminates all of the denominators.
This will result in 1600 = 25X.
You may now continue to solve the problem in which we divide both sides by 25.
We therefore get X = 64.
This means that 64% of 25 is 16, which means we need to remember
to write the percent symbol.
In example 2, it asks 14 is 60% of what.
Once again, we need to remember each of the pieces.
We have the "is" and the "of."
Remember "is" is the part and goes on top which we see here as 14.
We then look for the "of" which we do not know,
so we label it as X.
This will equal 60%.
Remember we write it as 60 over 100.
We can now solve the proportion by multiplying both sides by the LCD or 100X.
We proceed to reduce to clear the fractions.
We now have 1400 = 60X.
We can now divide both sides by 60
and this will give us X = 23.3 repeated percent.
Remember that it will either ask you to round
or you can write it as the exact as 23.3 with a bar
to show repeating percent equals X.
Remember in these types of problems that it is always "is" over "of"
equals percent over 100,
where "is" is your part over the "of" which is your whole.