1. Solve 4x + 7 = Solve 4x + 5 = 2x Write an expression for each: a. Twice the number n b. 5 more than x c. 7 less than y d. Twenty percent of b 5/4 x = 2 2n x + 5 y – b

 Solve simple algebraic problems  Increase efficiency in solving problems by applying algebraic reasoning skills

 In your studies of mathematics, you have had considerable experience solving problems. The following guideline can help to solve many algebra problems. Phase 1: UNDERSTAND the problem: What am I trying to find? What data am I given? Have I ever solved a similar one. Phase 2: Develop and carry out a PLAN : What strategies might I use to solve the problem? How can I correctly carry out the strategies? Phase 3: Find the ANSWER and CHECK : Does the proposed solution check? What is the answer to the problem? Does the answer seem reasonable? Have I stated the answer clearly?

The time that a traffic light remains yellow is 1 second more than 0.05 times the speed limit. What is the yellow time for a traffic light on a street with a speed limit of 30 mph. UNDERSTAND the problem Question: What is the time that the traffic light remains yellow? (classifying the question) UNDERSTAND the problem Question: What is the time that the traffic light remains yellow? (classifying the question) Data: The yellow time is 0.05 times the speed limit plus 1 second. (Identifying the data) Develop and carry out a plan: Choose a strategy. Write an equation:

Yellow Time is 1 second more than 0.05 times the speed limit y = x s y = s Translating into an equation For a speed limit of 30 mph, s will be 30. Thus we have the following: y = (30) y = y = 2.5

Find the ANSWER and CHECK On a 30 mph street, 2.5 seconds is a reasonable time for the light to remain yellow. The yellow time is 2.5 seconds Stating the answer clearly. Stating the answer clearly.

It has been found that the world record for the men’s 10,000 meter run has been decreasing steadily since The record is approximately minutes minus 0.05 times the number of year’s since Assume the record continues to decrease in this way. Predict what it will be in 2010 UNDERSTAND the problem Question: What will the record probably be in 2010? (classifying the question) UNDERSTAND the problem Question: What will the record probably be in 2010? (classifying the question) Data: The record was min in It decreases 0.05 times the number of years since (Identifying the data) Develop and carry out a plan: Choose a strategy. Write an equation:

Record is minutes minus 0.05 times the # of yrs R = – 0.05 x (2010 – 1950) Translating into an equation R = – 0.05(2010 – 1950) R = – 0.05(60) = Solving the equation Find the ANSWER and CHECK The number checks in the equation It is less than the original record and makes sense in the problem. We predict that the record in 2010 will be min. Stating the answer clearly.

a. The Country Cab Company charges 70¢ plus 12¢ per ¼ kilometer for each ride. What will be the total cost of a 14- km ride?

It has been found that the world record for the 800-m run has been decreasing steadily since The record is approximately 1.82 min minus the product of and the number of years since Predict what the record will be in 2010.

An insecticide originally contained ½ ounce of pyrethrums. The new formula contains ⅝ oz. of pyrethrums. What percent of the pyrethrums of the original formula does the new formula contain? UNDERSTAND the problem Question: What percent of the original amount of pyrethrums does the new formula contain? (classifying the question) UNDERSTAND the problem Question: What percent of the original amount of pyrethrums does the new formula contain? (classifying the question) Data: The original formula contained ½ oz, the new formula is ⅝ oz. (Identifying the data) Develop and carry out a plan: Choose a strategy. Write an equation:

We may translate to an equation and solve: What percent of ½ oz is ⅝ oz? Translating percent to “x 1/100” Multiplying Multiplying by the reciprocal of 1/200 y = 125

Find the ANSWER and CHECK We must find out whether 125% of ½ is ⅝. The number checks. This is reasonable, since ⅝ is greater than ½, the percent must be greater than 100. The amount of pyrethrins in the new formula, ⅝oz is 125% of the original amount of ½ oz. Stating the answer clearly.

A public television station set a goal of $350,000 in pledges during a certain month. The total pledged was $525,000. What percent of the station’s goal was reached?

A bread recipe calls for ⅔ cup of rye flour. You only have ¾ cup on hand. What percent of your original amount of rye flour will remain after baking the bread?

Textbook pg. 33 #2, 6, 7, 12 & 16