How can you use a proportion to solve a percent word problem? Explain in your own words.
To solve a percent word problem using a proportion, you need to set up a comparison between two ratios or fractions. This helps you find the unknown value or percent in the problem.
First, identify the information given in the problem. For example, you may be given the part and the whole, or the part and the percent.
Next, set up a proportion by comparing the two ratios or fractions. The unknown value or percent should be represented by a variable.
For example, let's say you want to find the percent increase of a stock price. If the original price is $100 and the new price is $120, you can set up a proportion like this:
(original price/100) = (new price/x)
Now, cross-multiply and solve for the unknown. In this case, you would multiply the original price and x, and equate it to 100 multiplied by the new price. Then, divide both sides of the equation to isolate the unknown value.
In our example, (100 * x) = (original price * 120).
Dividing both sides by the original price gives you x = 120.
So, the percent increase in this example is 20%.
By using a proportion, you establish a relationship between known values, and the unknown value is determined by solving for the variable. This method helps you find the solution to percent word problems.