Using Proportions To Solve Problems
However, the unknown quantity was different for each problem. Red is used for the unknown quantity in each problem.
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.
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.
This unknown quantity will be represented by x in our proportion. Substitute: Now we can substitute these values into our proportion.
becomes Solve: Cross multiply and we get: 20x = 800 Divide both sides by 20 to solve for x and we get: x = 40 Solution: 8 is 40% of 20. Note that in Problem 1 we did not have to cross multiply to solve the proportion.
Exponents may not be placed on numbers, brackets, or parentheses.
Parentheses ( ) and brackets [ ] may be used to group terms as in a standard equation or expression.
In Problem 1 we were asked 8 is what percent of 20?Use the following as a guide: Any lowercase letter may be used as a variable.Exponents are supported on variables using the ^ (caret) symbol. Note: exponents must be positive integers, no negatives, decimals, or variables.We will let variable x represent this unknown quantity in our proportion.Substitute: Now we can substitute these values into our proportion.and we found the solution by substituting into a proportion.But how would we solve this problem: 18 is 40% of what number? Identify: The phrase 18 is means that 18 is the part.and how would we solve this problem: What is 20% of 45? 40% means that 40 will replace percent in our proportion.The phrase of what number represents the whole and is the unknown quantity.20% means that 20 will replace percent in our proportion. Substitute: Now we can substitute these values into our proportion.becomes Solve: Cross multiply and we get: 100x = 45(20) or 100x = 900 Divide both sides by 100 to solve for x and we get: x = 9 Solution: 9 is 20% of 45 In Problems 1, 2 and 3 we are given two numbers and asked to find the third by using a proportion.