6.4 Ratio, Proportion and Variation 1.We will learn to solve proportions. 2.We will solve problems using proportions. 3.We will solve direction variation.

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Presentation transcript:

6.4 Ratio, Proportion and Variation 1.We will learn to solve proportions. 2.We will solve problems using proportions. 3.We will solve direction variation problems. 4.We will solve inverse variation problems.

Proportions We will learn to solve proportions

Solving Proportions

Solving Proportions

Applications of Proportions 1.Read the problem and represent the unknown quantity by x. 2.Set up a proportion by listing the given ratio on one side and the ratio with the unknown quantity on the other side. 1.Make sure that similar values are in numerators and similar values are in the denominators. 3.Drop units and apply the cross products principle. 4.Solve for x and answer the question. We will solve problems using proportions.

Example of aligning a proportion correctly

Example of aligning a proportion correctly Unwritten rule of local politics is that for every lawn sign you place you can count on 12 votes. How many votes can someone who places 220 lawn signs expect to receive?

Solving a Direct Variation Problem A person works for $12/hr. The person works 15 hours, how much money does he earn? We will solve direct variation problems.

Direct Variation in Geometry The two triangles above are known to be similar. Find the hypotenuse of the right triangle.

Direct Variation with Taxes Assuming the same tax rate, lets say you get your car tax bill on your old car. The town valued your car at $5500 and charged you $250. You want to buy a new car worth $22000, how much will your tax bill be?

Inverse Variation Inverse Variation – When we are talking about inverse variations we need to rearrange the quantities in the proportions. –Lets say we are going to Providence from NS. If we drive during rush hour we average 30mph and take 30 minutes to get there. If we drive at 2AM we average 60 mph and take 15 minutes to get there. We will solve inverse variation =

Example of Inverse Variation The heavier a vehicle is, the worse its gas mileage. A 4000 lb car averages 20 miles/gallon. How many miles/gallon would a 3000lb car get?

Example of Inverse Variation The loudness of a stereo speaker, measured in decibels, varies inversely as the square of your distance from the speaker. When you are 8 feet from the speaker, the loudness is 28 decibels. What is the loudness when you are 4 feet from the speaker?