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Equations for Speed and Investments

Solve various problems by completing tables and writing systems of equations, including finding the speed of a sailboat, determining investments in stocks and bonds, and finding the ages of individuals. Also solve problems involving flight speed and wind speed, and find the value of numbers based on their digits.

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Equations for Speed and Investments

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  1. Unit I Review Lessons 4 to 8

  2. Complete the table and write a system of equations A sailboat travels 24 mi. downstream in 3 h. The return trip upstream takes 4 hours. Find the speed of the sailboat in still water and the rate of the current.

  3. Complete the table and write a system of equations A sailboat travels 24 mi. downstream in 3 h. The return trip upstream takes 4 hours. Find the speed of the sailboat in still water and the rate of the current. 3(r + c) = 24 4(r – c) = 24 r = 7 mph, c = 1 mph

  4. Write and solve a system of equations Kathleen invests $12,000 in stocks and bonds. The stocks pay her 5.5% annual interest and the bonds pay 2.5% interest. If her annual income from the stocks and bonds is $420, how much is invested in stocks?

  5. Write and solve a system of equations Kathleen invests $8000 in stocks and bonds. The stocks pay her 5.5% annual interest and the bonds pay 2.5% interest. If her annual income from the stocks and bonds is $420, how much is invested in stocks? $4000 in stocks and $8000 in bonds

  6. Complete the table and write and solve a system of equations Gloria is 20 years older than Reggie. Five years ago she was five times as old as he was. How old is each now?

  7. Complete the table and write and solve a system of equations Gloria is 20 years older than Reggie. Five years ago she was five times as old as he was. How old is each now? G = R + 20 G – 5 = 5(R – 5) Answer: Gloria is 30 and Reggie is 10

  8. (2,3)

  9. Complete the table and write and solve a system of equations Jack’s age next year will be twice Bonnie’s age next year. Last year the sum of their ages was 32. How old is each now?

  10. Complete the table and write a system of equations Jack’s age next year will be twice Bonnie’s age. Last year the sum of their ages was 32. How old is each now? J + 1 = 2(B + 1) AND J – 1 + B – 1 = 32 ANSWER: Bonnie is 11, Jack is 23

  11. Complete table and write an equation or system of equations The 3000 km trip from New York to Wyoming takes 6 hours flying against the wind, but only 5.5 hours returning. Find the speed of the plane in still air and the wind speed.

  12. Complete table and write an equation or system of equations The 3000 km trip from New York to Wyoming takes 6 hours flying against the wind, but only 5.5 hours returning. Find the speed of the plane in still air and the wind speed. 6(r – w) = 3000 5.5(r + w) = 3000 r = 522 mph, w = 22 mph

  13. A number is ten times the sum of its digits. The tens digit is two greater than the units digit. Find the number.

  14. A number is ten times the sum of its digits. The tens digit is two greater than the units digit. Find the number. 10t + u = 10(t + u) t =u + 2 T = 2 and u = 0 so the number is 20

  15. The sum of the digits in a two-digit number is 7. The new number obtained when the digits are reversed is 27 less than the original number. Find the original number.

  16. The sum of the digits in a two-digit number is 7. The new number obtained when the digits are reversed is 27 less than the original number. Find the original number. t + u = 7 New number = original number – 27 10u + t = 10t + u – 27 Original number is 52

  17. The denominator of a fraction is 7 more than the numerator. If 5 is added to both the numerator and denominator, the value of the resulting fraction is ½. What is the original fraction.

  18. The denominator of a fraction is 7 more than the numerator. If 5 is added to both the numerator and denominator, the value of the resulting fraction is ½. What is the original fraction. d = 7 + n Answer: 2/9 n + 5 = 1 d + 5 2

  19. One number exceeds two times a second number by 2. The sum of twice the larger and five times the smaller is 40. What are the numbers? • A. Write a system of equations for the given data. Let x = the larger number, and y = the smaller number.

  20. x = 2y + 2 and 2x + 5y = 40 • One number exceeds two times a second number by 2. The sum of twice the larger and five times the smaller is 40. What are the numbers? • A. Write a system of equations for the given data. Let x = the larger number, and y = the smaller number. • Y = 4, x = 10

  21. The sum of two numbers is 24 and their difference is 8. What are the two numbers?

  22. The sum of two numbers is 24 and their difference is 8. What are the two numbers?

  23. Use the addition or subtraction method to solve the system 10x + 4y = 2 10x – 8y = 26

  24. Use the addition or subtraction method to solve the system 10x + 4y = 2 10x – 8y = 26 ANSWER: (1, -2)

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