# Algebra: Solving equations, graphing, inequalities, etc.

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15. A mathematics instructor asked her students to keep track of how much time each spent studying the chapter on percent notation in her basic mathematics course. She collected the information, together with test scores from that chapter's test, in the table below.

a). Use the two points reporting data for 9 hours of study time and 23 hours of study time and find a linear function that fits the data. (You can ignore the other lines of data in the chart.)

b.) Use the function to predict the test score of someone who has studied for 18 hours.

Study Time, x (in hours) Test Grade, y (in percent)

9 74

11 94

13 81

15 86

16 87

17 81

21 87

23 92

16. Define your variable and write an equation that could be used to solve the following problem. Do not solve the equation.

Josh left a 15% tip for a meal. The total cost of the meal, including the tip, was $30.50. What was the cost of the meal before the tip was added?

17. Define your variable and write an equation that could be used to solve the following problem. Do not solve the equation.

The product of two consecutive odd integers is 255. Find the integers.

18. Define your variables and write a system of equations that could be used to solve the following problem. Do not solve the equations.

Madeline goes to a bank and gets change for a $50 bill consisting of all $5 bills and $1 bills. There are 22 bills in all. How many of each kind are there?

19. Solve 3(r - 6) + 2 > 4(r + 2) - 21 and express the solution as a graph, using solution set notation, and using interval notation.

20. Graph 2x + 3y ≥ 6.

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The solution consists of complete explanations and answers to five algebra questions involving solving equations, graphing, inequalities, and word problems.

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15. A mathematics instructor asked her students to keep track of how much time each spent studying the chapter on percent notation in her basic mathematics course. She collected the information, together with test scores from that chapter's test, in the table below.

a). Use the two points reporting data for 9 hours of study time and 23 hours of study time and find a linear function that fits the data. (You can ignore the other lines of data in the chart.)

We use two points (9, 74) and (23, 92) to find a linear function as ...

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