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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.

Solution Preview

(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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