The Number of Coins Adding Up to a Fixed Amount
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Consider the following problem. Provide evidence for each answer.
A collections of k coins consists of nickels, dimes, and quarters, and has a value of 5c cents. The numbers k and c are positive integers. How many coins of each kind are there?
(a) Write a system of two equations in three unknowns which models the solution to the problem.
(b) Is the system always consistent? If not, what conditions of c and k make it consistent?
(c) Cam the system have a unique solution? Explain in detail.
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Solution Summary
This solution shows how to compute the number of nickels, dimes and quarters which can add up to a fixed amount of money.
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(a) Let n be the number of nickels, d the number of dimes, and q the number of quarters. Then we have
n + d + q = k
5n + 10d + 25q = 5c
The second equation can be reduced to
n + 2d + 5q = ...
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