§ 4.4

1. § 4.4 Solving Applied Problems Involving Proportions

2. Problem Solving Steps • Understand the problem. • Read the problem carefully. • Draw a picture if this is helpful. • Fill in the Mathematics Blueprint so that you have the facts and a method of proceeding in this situation. • Solve and state the answer. • Perform the calculations. • State the answer, including the unit of measure. • Check. • Estimate the answer. • Compare the exact answer with the estimate to see if your answer is reasonable.

3. Mathematics Blueprint for Problem Solving Gather the Facts What Am I Asked to Do? How Do I Proceed? Key Points to Remember Mathematics Blueprint The Mathematical Blueprint is simply a sheet of paper with four columns. Each column tells you something to do.

4. Find the number of runs in 9 innings. 52 runs were given up in 260 innings. Set up a proportion comparing runs to innings Mathematics Blueprint Example: A baseball pitcher gave up 52 earned runs in 260 innings of pitching. At this rate, how many runs would he give up in a 9-inning game? (This decimal is called the pitcher’s earned run average.) Mathematics Blueprint for Problem Solving Gather the Facts What Am I Asked to Do? How Do I Proceed? Key Points to Remember One fraction represents the total innings and one represents the 9 innings. Example continues.

5. Mathematics Blueprint A baseball pitcher gave up 52 earned runs in 260 innings of pitching. At this rate, how many runs would he give up in a 9-inning game? (This decimal is called the pitcher’s earned run average.) The pitcher will give up 1.8 runs in a 9-inning game.

6. Find the total cost for the paint. 2 gal per 750 sq. ft.; 7875 sq. ft. total to be painted; cost is 8.50 per gallon Set up a proportion comparing gals to ft.; multiply the answer by $8.50. Mathematics Blueprint Example: It is recommended that 2 gallons of paint are used for every 750 square feet of wall. A painter is going to paint 7875 square feet of wall with a paint that costs $8.50 per gallon. How much will the painter spend for paint? Mathematics Blueprint for Problem Solving Gather the Facts What Am I Asked to Do? How Do I Proceed? Key Points to Remember One fraction represents the recommended paint and one represents the needed paint. Example continues.

7. 21 gallons of paint will be needed. Mathematics Blueprint It is recommended that 2 gallons of paint is used for every 750 square feet of wall. A painter is going to paint 7875 square feet of wall with a paint that costs $8.50 per gallon. How much will the painter spend for paint? The total cost for the paint is $178.50.