Math 6 Honors Periods 6 & 7

Problem Solving: Using Proportion 7-8

Proportions can be used to solve word problems. Use the following steps to help you in solving problems using proportions

Ø Decide which quantity is to be found and represent it by a variable

Ø Determine whether the quantities involved can be compared using ratios (rates)

Ø Equate the ratios in a proportion

Ø Solve the proportion

Some guidelines you can use to determine when it is appropriate to use a proportion to solve a word problem.

Ask the following questions

If one quantity increase does the other quantity also increase? (If one quantity decreases, does the other quantity decrease?) When the number of tires is increase, the cost is also increased.

Does the amount of change (increase or decrease) o one quantity depend upon the amount of change (increase or decrease) of the other quantity? The amount of increase in the cost depends upon the number of additional tires bought.

Does one quantity equal some constant times the other quantity? The total costs equals the cost of one tire times the number of tires. The cost of one tire is constant.

If the answers to all the questions above is YES, then it is appropriate to use a proportion.

Sometimes setting up a table can be useful

Number of tires	Cost
4	$264
5	c

4c = 5(264)

Although the problems in this lesson may be solved with out using proportions, I must insist that you write a proportion for each problem and solve using this method. You may check your work using another other method you know.

Scale Drawing 7-9

Opening your books to page 237, you will notice a drawing of a house. In this drawing of the house, the actual height of 9 meters is represented by a length of 3 centimeters, and the actual length of 21 meters is represented by a length of 7 centimeters.

This means that 1 cm in the drawing represents 3 m in the actual building. Such a drawing in which all lengths are in the same ratio to actual lengths is called a scale drawing.

The relationship of length in the drawing to actual length is called the scale. In the drawing of the house the scale is 1cm: 3m

We can express the scale as a ratio, called the scale ratio, if a common unit of measure is used. Since 3 m = 300 cm, the scale ratio is 1/300

Using the book’s drawing on page 237, find the length and width of the room shown, if the scale of the drawing is 1cm: 1.5 m

Measuring the drawing, we find that it has a length of 4 cm and a width of 3 cm