Solving Percent Problems Using Proportions

In the example of 5The amount is the number that relates to the percent. Once you have an equation, you can solve it and find the unknown value.To do this, think about the relationship between multiplication and division.

In the example of 5The amount is the number that relates to the percent. Once you have an equation, you can solve it and find the unknown value.To do this, think about the relationship between multiplication and division.For example, 60% = \(\frac\) and we can simplify \(\frac = \frac\).

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The proportion method for solving percent problems involves a percent proportion.

A percent proportion is an equation where a percent is equal to an equivalent ratio.

Using the vocabulary we used earlier: $$\begin \frac & = \frac \\ \frac & = \frac \end$$ (a) After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

(b) Overall, after looking at the checklist, do you think you are well-prepared for the next Chapter?

Look at the pairs of multiplication and division facts below, and look for a pattern in each row.

Percent problems can also be solved by writing a proportion.Example 47% of the students in a class of 34 students has glasses or contacts.How many students in the class have either glasses or contacts?Find a percentage or work out the percentage given numbers and percent values. The formulas below are all mathematical variations of this formula. X and Y are numbers and P is the percentage: There are nine variations on the three basic problems involving percentages.Use percent formulas to figure out percentages and unknowns in equations. See if you can match your problem to one of the samples below.Jeff wonders how much money the coupon will take off the original 0 price.In a percent problem, the base represents how much should be considered 100% (the whole); in exponents, the base is the value that is raised to a power when a number is written in exponential notation. Since the percent is the percent off, the amount will be the amount off of the price.$$\frac=\frac$$ $$\frac\cdot =\frac\cdot b$$ $$a=\frac\cdot b$$ x/100 is called the rate.$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$ Where the base is the original value and the percentage is the new value.$$a=r\cdot b$$ $\%=0.47a$$ $$=0.47\cdot 34$$ $$a=15.98\approx 16$$ 16 of the students wear either glasses or contacts.We often get reports about how much something has increased or decreased as a percent of change.