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Identify: 18 is the part and will replace IS in our proportion.
PERCENT is the unknown quantity in our proportion, to be represented by n.
Substitute: becomes Solve: Cross multiply and we get: 56n = 14(100), or 56n = 1400 Divide both sides by 56 and we get: n = 25 Solution: 25% of 56 is 14 Problem 6: 18 is 75% of what number?
We need to figure out how to find this unknown quantity. Similarly, in the statement, "One number is some percent of another number.", the phrase "one number" represents the part and "another number" represents the whole.
Every statement of percent can be expressed verbally as: "One number is some percent of another number." Percent statements will always involve three numbers. Thus the statement, "One number is some percent of another number.", can be rewritten: "One number is some percent of another number.", becomes, "The part is some percent of the whole." From previous lessons we know that the word "is" means equals and the word "of" means multiply.
In previous lessons, you were shown how to convert a decimal to a percent and a percent to a decimal.
Thus, if you were asked to Find 15% of 120, you would multiply .15 by 120, to get an answer of 18.becomes Solve: Cross multiply and we get: 100p = 52(25) or 100p = 1300 Divide both sides by 100 to solve for p and we get: p = 13 Solution: 13 is 25% of 52 Note that we could restate this problem as, "Find 25% of 52", and get the same answer.However, in the interest of consistency, we will use proportions to solve percent problems throughout this lesson.In Problems 5 through 7, we will use n to represent the unknown quantity. Identify: 56 is the whole and will replace OF in our proportion.14 is the part and will replace IS in our proportion.Note that in all three percent statements, the whole always follows the word "of" and the part always precedes the word "is".This is not surprising since our original statement is, "One number is some percent of another number." Thus, we can revise our proportion as follows: becomes Let's solve some more percent problems using proportions. Identify: 25% means that 25 will replace PERCENT in our proportion.In Problem 1 we were asked 8 is what percent of 20?and we found the solution by substituting into a proportion.But what would you do if you given this problem: 8 is what percent of 20?In this problem, the percent is the unknown quantity! Looking at this problem, it is clear that 8 is the part and 20 is the whole.