Solving Problems With Proportions Concentration Camp Essays
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.
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. Problem 1: If 8 out of 20 students in a class are boys, what percent of the class is made up of boys?
We could have used equivalent fractions instead (i.e., since 20 multiplied by 5 equals 100, we get that 8 multiplied by 5 equals x, so x equals 40).
In Problem 1 we were asked 8 is what percent of 20?
In Problem 1 we let x represent the unknown quantity "what percent"; in Problem 2 we let x represent the unknown quantity "of what number"; and in Problem 3 we let x represent the unknown quantity "What is." Thus, we solved three different percent problems, where in each problem, two numbers were given and we were asked to find the third.The percent is the unknown quantity in this problem. Identify: The phrase 8 is means that 8 is the part.The phrase what percent tells us that percent is the unknown quantity.$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$ Where the base is the original value and the percentage is the new value.Example 47% of the students in a class of 34 students has glasses or contacts.There are two different methods that we can use to find the percent of change.We begin by subtracting the smaller number (the old value) from the greater number (the new value) to find the amount of change.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.How many students in the class have either glasses or contacts?$$a=r\cdot b$$ $\%=0.47a$$ $$=0.47\cdot 34$$ $$a=15.98\approx 16$$ 16 of the students wear either glasses or contacts.