These are practice problems dealing with money, designed to be used in an elementary algebra class.

1. Section 3.4 Money Problem Practice Image Courtesy of Amarand Agasi

2. Instructions This presentation contains five problems similar to the money problems in section 3.4. Try each problem, then check your work against mine. If you get stuck you can peek ahead as far as you need to, but try to finish the problem on your own. Remember to define your variable and create a meaningful algebraic equation for each problem.

3. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065?

4. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Analyze the information given and decide what your variable is going to represent.

5. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Analyze the information given and decide what your variable is going to represent. We will use the Simple interest formula: I = Prt

6. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Analyze the information given and decide what your variable is going to represent. Because we do no know how much was invested in either account we will need to use a variable to represent one of the two principals. All of the money that is not in the first account is in the second, thus $18000-x

7. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Use the information you have collected to create a meaningful algebraic equation.

8. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Use the information you have collected to create a meaningful algebraic equation. The total interest is the sum of the interest earned by both accounts. 0.065x+0.05(18000-x)=1065

9. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Solve your equation. 0.065x+0.05(18000-x)=1065

10. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Solve your equation. 0.065x+0.05(18000-x)=1065

11. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Answer the question asked.

12. Problem #1 Jared Brooks invested $18,000, part at 6.5% simple interest and the rest at 5% simple interest for a period of 1 year. How much did he invest at each rate if the total annual interest earned was $1065? Answer the question asked. x = 11000 is the amount of money in the 6.5% account. 18000-11000=7000 is the amount in the 5% account. He invested $11,000 at 6.5% interest and $7000 at 5% interest.

13. Problem #2 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate?

14. Problem #2 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Analyze the information given and decide what your variable is going to represent.

15. Problem #2 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Analyze the information given and decide what your variable is going to represent. We will use the Simple interest formula: I = Prt

16. Problem #1 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Analyze the information given and decide what your variable is going to represent. Because we do no know how much was invested in either account we will need to use a variable to represent one of the two principals. All of the money that is not in the first account is in the second, thus $11875-x

17. Problem #1 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Use the information you have collected to create a meaningful algebraic equation.

18. Problem #2 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Use the information you have collected to create a meaningful algebraic equation. Because each account earned the same amount of interest, I set the two quantities equal to each other. 0.04x = 0.055(11875-x)

19. Problem #2 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Solve your equation. 0.04x = 0.055(11875-x)

20. Problem #1 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Solve your equation. 0.04x = 0.055(11875-x)

21. Problem #1 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Answer the question asked.

22. Problem #2 Shawna invested $11875, part at 4% and part at 5.5% simple interest for a period of one year. If both investments earned the same amount of interest, how much did she invest at each rate? Answer the question asked. x = 6875 is the amount of money in the 4% account. 11875-6875 = 5000 is the amount in the 5.5% account. She invested $6,875 at 4% interest and $5,000 at 5.5% interest.

23. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold?

24. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Analyze the information given and decide what your variable is going to represent

25. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Analyze the information given and decide what your variable is going to represent

26. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Analyze the information given and decide what your variable is going to represent Because we don’t know the quantity of either we just pick one of either regular quantity or student quantity for our variable to represent. I pick R as my variable to represent the quantity of regular tickets sold. Also, every ticket sold what wasn’t at the Regular rate was at the student rate, so the other quantity will be 310 –R.

27. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Use the information you have analyzed to create a meaningful algebraic equation.

28. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Use the information you have analyzed to create a meaningful algebraic equation. Because $2045 is the total for the matinee, I will add the quantities of money collected for each type of ticket. 8R+5(310-R)=2045

29. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Solve the equation you have found. 8R+5(310-R)=2045

30. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Solve the equation you have found. 8R+5(310-R)=2045

31. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Answer the question asked.

32. Problem #3 A movie theater charges $8 for regular admission and $5 for student admission for a matinee. One day the theater sold 310 tickets for a matinee and took in $2045. How many of each type of admission was sold? Answer the question asked. There were 165 regular admissions, thus there must have been 310-165=145 student admissions sold. Answer: 165 Regular and 145 Student

33. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job?

34. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Analyze the information given and decide what your variable is going to represent.

35. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Analyze the information given and decide what your variable is going to represent.

36. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Analyze the information given and decide what your variable is going to represent. Because we don’t have the hours worked at either job, we need to use a variable to represent this. My variable, n, will represent the hours worked at the $9/hour job. The hours she didn’t work at that job were worked at the other job, thus 32-n hour were worked at $11/hour.

37. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Use the information you have gathered in a meaningful algebraic equation.

38. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Use the information you have gathered in a meaningful algebraic equation. Her total pay for the week is the pay for each job added together. 9n+11(32-n)=324

39. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Solve your equation. 9n+11(32-n)=324

40. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Solve your equation. 9n+11(32-n)=324

41. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Answer the question asked.

42. Problem #4 Parminder has two part-time jobs. One job pays $9 per hour and the other pays $11 per hour. Last week she worked a total of 32 hours and earned a total of $324. How many hours did she work at each job? Answer the question asked. n=14 is the number of hours at the $9/hour job, thus 32-14 = 18 is the number of hours at the other job. Answer: She worked 14 hours at the $9/hour job and 18 hours at the $11/hour job.

43. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar?

44. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Analyze the information given and decide what your variable is going to represent.

45. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Analyze the information given and decide what your variable is going to represent.

46. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Analyze the information given and decide what your variable is going to represent. We need to know how many pennies and nickels we have, so we’ll assign our variable to represent one of the two quantities. Let’s let our variable, p, be the number of pennies. This means that all the rest of the coins (120-p) are nickels.

47. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Use the information you have gathered in a meaningful algebraic equation.

48. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Use the information you have gathered in a meaningful algebraic equation. We know the total value of the coins is $2.20. The total value of the coins is also the sum of the values of each type of coin. 0.01p + 0.05(120-p) = 2.20

49. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Solve your equation. 0.01p + 0.05(120-p) = 2.20

50. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Solve your equation. 0.01p + 0.05(120-p) = 2.20

51. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Answer the question asked.

52. Problem #5 Michelle has jar in which she places all of her pennies and nickels. The jar currently contains 120 coins which have a value of $2.20. How many of each type of coin does she have in the jar? Answer the question asked. We know that p = 95 is the number of pennies. To find the number of nickels we can subtract this number from the total 120-95 = 25. Answer: 95 pennies and 25 nickels.