Warm Up # 1

Solve (Show each step)

-5x + 14 ≥ 8x - 25

Warm Up # 2

Car-Go Rentals charges $30 per day plus 28 cents per mile to rent an economy car. Rapid Rent charges $50 for one day and 15 cents per mile. The Winderwere family is going to rent a car for 2 days while on vacation. For how many miles will Car-Go be the better value??

Linear CombinationsIn many situations, a multiple of one variable is

added to a multiple of another variable, creating a linear combination of variables.

High schools and colleges grades in courses are summarized by a grade point average (GPA).To calculate a GPA, you give each letter grade a point value:• A = 4 points• B = 3 points• C = 2 points• D = 1 point• F = 0 points

Suppose a student took 20 semester courses over 2 high school years and received 5 A’s, 11 B’s, 4 C’s, and no D’s or F’s

Letter Grade

Value Frequency of Grade Value

A 4 5 5 • 4 = 20

B 3 11 11 • 3 = 33

C 2 4 4 • 2 = 8

D 1 0 0 • 1 = 0

F 0 0 0 • 1 = 0

TOTAL 20 61

The student has a total of 61 points 20 courses. GPA is calculated by dividing the total number of points by the number of courses.

GPA = 61/20 or 3.05

Letter Grade

Value Frequency of Grade Points

A 4 a 4a

B 3 b 3b

C 2 c 2c

D 1 d 1d

F 0 f 0f

TOTALS a + b + c + d + f 4a + 3b + 2c + 1d + 0f

A school has to calculate GPA’s for all students. To do this without having to calculate each individual by hand, so we use a general form to accomplish this.

A school organized a fund raiser to raise money for the school library. Each class sold boxes of mixed nuts for $3.00 each and rolls of wrapping paper for $4.00 each. One class collected $127 but forgot to record how many of each item they sold. Write an equation the class could use to determine how many boxes of nuts and how many rolls of paper they sold.

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LINEAR COMBINATIONS IN REAL LIFE:

The value of money you have in your pocket is a linear combination of the number of pennies, nickels, dimes, quarters, dollar-bills, and so on that you have.

Suppose you have less than $5.00 in quarters and dimes. Find an inequality to describe how many of each you might have??

At a garage sale, magazines sold for $0.10 and books sold for $0.25. Kareem spent $2.35 on magazines and books.

• Write an equation relating the number of magazines m, the number of books b, and the total amount spent by Kareem.

• Find a solution for this situation