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.

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  1. So, you come up with the great idea to show a film. You plan to dim the lights, hit the play button, and quietly sit in the back of the classroom wishing for some popcorn. The film starts and before you know it you find yourself wondering – how does this fit with the material I’ve been presenting?

  2. Odds are, you’ll sound like Rutger Hauer talking about moon beams and tears in the rain; it may sound beautiful but your audience has little to relate to. [Note to readers: I’m not against pure cinema; I just generally can’t handle it for more than thirty minutes and I find it difficult to write about.] The plot may be minimal and the film may primarily define itself visually but those two factors intersect to provide the film with a multi-layered subtext.