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Integer Solutions to Linear Systems: Although a linear system may have an infinite number of solutions, it is possible that we are only interested in those solutions where all the variables are integers. This could happen, for example, when the variables represent objects being counted. Consider the following: A jar containing 98 coins consisting only of dimes (worth 10 cents each), nickels (worth 5 cents each) and pennies (worth 1 cent each). The total value of the coins is $ 6.49. а. Set up the system of equations representing this system, in the variables d, n, and p. b. Find the rref of this system. If you did (b) correctly, p should be a free variable. Solve for d and n in terms of p, as usual, then find the smallest positive integer value for p that will make both d and n positive integers. Use trial and error, if need be. This gives one possible solution to the system, but not necessarily the only one. Find the solution with the largest number of pennies. с. d.

Integer Solutions to Linear Systems: Although a linear system may have an infinite number of solutions, it is possible that we are only interested in those solutions where all the variables are integers. This could happen, for example, when the variables represent objects being counted. Consider the following: A jar containing 98 coins consisting only of dimes (worth 10 cents each), nickels (worth 5 cents each) and pennies (worth 1 cent each). The total value of the coins is $ 6.49. а. Set up the system of equations representing this system, in the variables d, n, and p. b. Find the rref of this system. If you did (b) correctly, p should be a free variable. Solve for d and n in terms of p, as usual, then find the smallest positive integer value for p that will make both d and n positive integers. Use trial and error, if need be. This gives one possible solution to the system, but not necessarily the only one. Find the solution with the largest number of pennies. с. d.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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9. Integer Solutions to Linear Systems: Although a linear system may have an infinite number of solutions, it is possible that we are only interested in those solutions where all the variables are integers. This could happen, for example, when the variables represent objects being counted. Consider the following: A jar containing 98 coins consisting only of dimes (worth 10 cents each), nickels (worth 5 cents each) and pennies (worth 1 cent each). The total value of the coins is $ 6.49. Set up the system of equations representing this system, in the variables d, n, and p. Find the rref of this system. а. b. If you did (b) correctly, p should be a free variable. Solve for d and n in terms of p, as usual, then find the smallest positive integer value for p that will make both d and n positive integers. Use trial and error, if need be. This gives one possible solution to the system, but not necessarily the only one. Find the solution with the largest number of pennies. с. d.
Transcribed Image Text:9. Integer Solutions to Linear Systems: Although a linear system may have an infinite number of solutions, it is possible that we are only interested in those solutions where all the variables are integers. This could happen, for example, when the variables represent objects being counted. Consider the following: A jar containing 98 coins consisting only of dimes (worth 10 cents each), nickels (worth 5 cents each) and pennies (worth 1 cent each). The total value of the coins is $ 6.49. Set up the system of equations representing this system, in the variables d, n, and p. Find the rref of this system. а. b. If you did (b) correctly, p should be a free variable. Solve for d and n in terms of p, as usual, then find the smallest positive integer value for p that will make both d and n positive integers. Use trial and error, if need be. This gives one possible solution to the system, but not necessarily the only one. Find the solution with the largest number of pennies. с. d.
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