Algebra 21.6

Pinkston

SAT QuestionWhat is the greatest possible sum of three consecutive even integers whose product is zero?A.-6B.-3C.0D.3E.6

Zero has to be one of the numbers, so the possibilities are:

-4, -2, 0-2, 0, 20, 2, 4

The one that gives the greatest sum is the last one: sum is 6.

Solving Word Problems

In Algebra County

Write HeadingWrite EquationSolve EquationWrite Solution asked for

On Wednesday, Harry picked 3 times as many quarts of berries as on Tuesday. On Thursday, he picked 5 times as many quarts as on Tuesday. In all he picked 153 quarts. Find the number he picked each day.

The heading defines the variables needed to solve the problem.

x is the variable we know the least about.

On Wednesday, Harry picked 3 times as many quarts of berries as on Tuesday. On Thursday, he picked 5 times as many quarts as on Tuesday. In all he picked 153 quarts. Find the number he picked each day.

For this problem, we need to make variables for:TuesdayWednesdayThursday

Which one do we know the least about?

x3x

5x

On Wednesday, Harry picked 3 times as many quarts of berries as on Tuesday. On Thursday, he picked 5 times as many quarts as on Tuesday. In all he picked 153 quarts. Find the number he picked each day.

“In all” means add up all the variables for each day.

3 5 153x x x

3 5 153x x x 9 153x 9 9

17x Now, go back to the heading to write all the solutions asked for.

On Wednesday, Harry picked 3 times as many quarts of berries as on Tuesday. On Thursday, he picked 5 times as many quarts as on Tuesday. In all he picked 153 quarts. Find the number he picked each day.

For this problem, we need to make variables for:TuesdayWednesdayThursday

x3x

5x

17 quarts of berries3(17) 51 .qts

5(17) 85 .qts

TuesdayWednesdayThursday

x3x

5x

17 berries3(17) 51 berries

5(17) 85 berries

We can check it by adding the three answers together

to see if we get 153.

Example 2

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 mi/h? Heading:

x = yellow timey = speed limit

Equation:x = 1+.05y (Substitute 30 for y)x =1+.05(30)

Solve:x =1+.05(30)x = 2.5

Write solution:2.5 sec.

Example 3

It has been found that the world record for the men’s 10,000 meter run has been decreasing steadily since 1950. The record is approx. 28.87 minutes minus .05 times the number of years since 1950. Assume the record continues to decrease in this way. Predict what it will be in 2010.

Heading:x = world recordy = years since 1950

Equation:x = 28.87 - .05y

Solve:x = 28.87 - .05ySubstitute 60 for yx = 25.87

Write solution:25.87 min.

To find the percent of increase or decrease:

Amount of increase or decreaseOriginal number

Example 3:16/p. 33. In 1995 the average American ate 48.8 lb of chicken. This was 6.3 lb more than the average in 1990. What was the percent of increase in chicken consumption from 1990 to 1995?

Amount of increase or decrease Original number

6.3 42.5

= 48.8 – 6.3 14.8%

In 1990 In 1995

48.8

Increase

?? 6.3

SAT QuestionIf x and y are negative integers, which of the following must be positive?A. x + yB. x – yC. y – xD. – (x – y)E. – (x + y)

A. (-) + (-) is negativeB. (-) – (-) could be negative

or positiveC. Same as aboveD. - [(-) - (-)] could be eitherE. - [(-) + (-)] is definitely

positive!

Classwork:

2, 8, 12, 16 / 33

Get ready for a “Small Quiz” to be written

on your grade sheet.

Solve and write answer in set notation:1.

2.

Quiz. Copy the problems and write the answer.

Put your grade paper on the front of your row, quiz side down.

37

5x

5 3 11a a

THE END