Translating and Solving Basic Percent Equations

Translating and Solving Basic Percent Equations

We will solve percent equations using the methods we used to solve equations with fractions or decimals. Without the tools of algebra, the best method available to solve percent problems was by setting them up as proportions. Now as an algebra student, you can just translate English sentences into algebraic equations and then solve the equations.

We can use any letter you like as a variable, but it is a good idea to choose a letter that will remind us of what you are looking for. We must be sure to change the given percent to a decimal when we put it in the equation.

Example

Translate and solve: What number is 35% of 90?

Solution

Translate into algebra. Let \(n\)= the number.
Remember "of" means multiply, "is" means equals.
Multiply.
	\(31.5\) is \(35%\) of \(90\)

We must be very careful when we translate the words in the next example. The unknown quantity will not be isolated at first, like it was in the example above. We will again use direct translation to write the equation.

Example

Translate and solve: 6.5% of what number is $1.17?

Solution

Translate. Let \(n=\) the number.
Multiply.
Divide both sides by 0.065 and simplify.
	\(6.5%\) of \(\$18\) is \(\$1.17\)

In the next example, we are looking for the percent.

Example

Translate and solve: 144 is what percent of 96?

Solution

Translate into algebra. Let \(p=\) the percent.
Multiply.
Divide by 96 and simplify.
Convert to percent.
	\(144\) is \(150%\) of \(96\)

Note that we are asked to find percent, so we must have our final result in percent form.