2. You have some coins, each of which is a penny (1 cent), a nickel (5 cents), a dime (10 cents), a quarter (25 cents), or a half-dollar (50 cents). You know that • you have three times as many dimes as quarters, the number of pennies and nickels combined is one more than the number of dimes and quarters combined, you have 13 coins in total, and the total value of your coins is $2.68 (268 cents). (a) Set up (do not solve) a system of linear equations for the numbers of pennies (p), nickels (n), dimes (d), quarters (q), and half-dollars (h) you have. (b) Write down the augmented matrix corresponding to your linear system from part (a). (c) Is it possible that there a unique solution (where p, n, d, q, and h are real numbers) to your linear system from part (a)? Answer yes or no (no justification necessary).
2. You have some coins, each of which is a penny (1 cent), a nickel (5 cents), a dime (10 cents), a quarter (25 cents), or a half-dollar (50 cents). You know that • you have three times as many dimes as quarters, the number of pennies and nickels combined is one more than the number of dimes and quarters combined, you have 13 coins in total, and the total value of your coins is $2.68 (268 cents). (a) Set up (do not solve) a system of linear equations for the numbers of pennies (p), nickels (n), dimes (d), quarters (q), and half-dollars (h) you have. (b) Write down the augmented matrix corresponding to your linear system from part (a). (c) Is it possible that there a unique solution (where p, n, d, q, and h are real numbers) to your linear system from part (a)? Answer yes or no (no justification necessary).
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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Transcribed Image Text:2. You have some coins, each of which is a penny (1 cent), a nickel (5 cents), a dime (10 cents), a quarter
(25 cents), or a half-dollar (50 cents). You know that
• you have three times as many dimes as quarters,
• the number of pennies and nickels combined is one more than the number of dimes and quarters
combined,
• you have 13 coins in total,
• and the total value of your coins is $2.68 (268 cents).
(a) Set up (do not solve) a system of linear equations for the numbers of pennies (p), nickels (n), dimes (d),
quarters (q), and half-dollars (h) you have.
(b) Write down the augmented matrix corresponding to your linear system from part (a).
(c) Is it possible that there a unique solution (where p, n, d, q, and h are real numbers) to your linear system
from part (a)? Answer yes or no (no justification necessary).
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