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# Linear Combinations

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### Linear Combinations

1. 1. Warm Up # 1 <br />Solve (Show each step)<br />-5x + 14 ≥ 8x - 25<br />
2. 2. Warm Up # 2<br />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??<br />
3. 3. Linear Combinations<br />In many situations, a multiple of one variable is added to a multiple of another variable, creating a linear combination of variables. <br />
4. 4. High schools and colleges grades in courses are summarized by a grade point average (GPA).<br />To calculate a GPA, you give each letter grade a point value:<br /><ul><li> A = 4 points
5. 5. B = 3 points
6. 6. C = 2 points
7. 7. D = 1 point
8. 8. F = 0 points </li></ul>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<br />
9. 9. 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. <br />GPA = 61/20 or 3.05 <br />
10. 10. 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. <br />
11. 11. 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.<br /> One class collected \$127 but forgot to record how many of each item they sold. <br /> Write an equation the class could use to determine how many boxes of nuts and how many rolls of paper they sold. <br />
12. 12.
13. 13. LINEAR COMBINATIONS IN REAL LIFE:<br />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. <br />
14. 14. Suppose you have less than \$5.00 in quarters and dimes. Find an inequality to describe how many of each you might have??<br />
15. 15. At a garage sale, magazines sold for \$0.10 and books sold for \$0.25.<br /> Kareem spent \$2.35 on magazines and books. <br /><ul><li> Write an equation relating the number of magazines m, the number of books b, and the total amount spent by Kareem.
16. 16. Find a solution for this situation</li></li></ul><li>