word problems 2

Percent and Proportions 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. 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! We need to figure out how to find this unknown quantity. Every statement of percent can be expressed verbally as: " One number is some percent of another number. " Percent statements will always involve three numbers. For example: ____ is ____ % of ____ . In the problem, 8 is what percent of 20?, the number 8 is some percent of the number 20. Looking at this problem, it is clear that 8 is the part and 20 is the whole. 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. 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. Thus, we can rewrite the statement above: The statement: "The part is some percent of the whole." , becomes the equation: the part = some percent x the whole Since a percent is a ratio whose second term is 100, we can use this fact to rewrite the equation above as follows: the part = some percent x the whole becomes: the part = x the whole Dividing both sides by "the whole" we get the following proportion: Since percent statements always involve three numbers, given any two of these numbers, we can find the third using the proportion above. Let's look at an example of this. Problem 1: If 8 out of 20 students in a cl ass are boy s, wh at perce nt of the class i s made up of boys? Analysis: In this problem, you are being asked 8 is what percent of 20? You are given two numbers from the proportion above and asked to find the third. The percent is the unknown quantity in this problem. We need to find this unknown quantity. Identify: The phrase 8 is means that 8 is the part. The phrase what percent tells us that percent is the unknown quantity. This unknown quantity will be represented by x in our proportion. The phrase of 20 means that 20 is the whole. Substitute: Now we can subst itute these values into our proportion.

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