How To Solve Percent Problems Using Proportions Financial Planning For Small Business Owners
Example Use cross product to determine if the two ratios form a proportion.$$\frac,\: \: \frac$$ $$\frac\overset \frac$$ $$\frac\cdot 16\cdot 40\overset \frac\cdot 16\cdot 40$$ $$\frac\cdot\cdot 40\overset \frac\cdot 16\cdot $$ $\cdot 40\overset5\cdot 16$$ $=80$$ Here we can see that 2/16 and 5/40 are proportions since their cross products are equal.
A proportion is an equation that says that two or more ratios are equal.$$a=r\cdot b\Rightarrow Percent=Rate\cdot Base$$ 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. So they are easier to compare than fractions, as they always have the same denominator, 100. The amount saved is always the same portion or fraction of the price, but a higher price means more money is taken off.Interest rates on a saving account work in the same way.To solve problems with percent we use the percent proportion shown in "Proportions and percent".$$\frac=\frac$$ $$\frac\cdot =\frac\cdot b$$ $$a=\frac\cdot b$$ x/100 is called the rate.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.The more money you put in your account, the more money you get in interest.It’s helpful to understand how these percents are calculated.