Problems Involving Coin

The problems involving coins (also referred to as the Frobenius coins problem or Frobenius problem, after the mathematician Ferdinand Frobenius) is a mathematical problem that asks what is the largest monetary amount that cannot be obtained using only coins of specified denominations. For example, the largest amount that cannot be obtained using only coins of 3 and 5 units is 7 units. The solution to this problem for a given set of coin denominations is called the Frobenius number of the set. In this article we shall disuss about problem involving coins.

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Problems involving coins example

Problems involving coins example 1:

There are 3 times as a lot of nickels as quarters, and one-half as a lot of dimes as nickels, Find out how many coins of each type are there, If collection of 25 coins, includes  dimes, nickels, and quarters, has a value of $3.30.

Assigning the variables

The number of quarters: q

The number of nickels: 3q

The number of dimes: (½)(3q) = (3/2)q

There are a total number of 25 coins, therefore:

q + 3q + (3/2)q = 25

4q + (3/2)q = 25

8q + 3q = 50

11q = 50

q = 6

Then there are 6 quarters, 9 dimes and 10 nickels.

Problems involving coins example 2:

A bag have the equal number of pennies, nickels, and dimes. The coins total $1.70. How many of each type of coin bag contain?

There is the equal number of  type of coin, use variable to place for each:

The number of pennies: q

The number of nickels: q

The number of dimes: q

The value of the coin is,  the number of cent for each coin times the number of that type of coin, so:

The Value of pennies: 1q

The value of nickels: 5q

The value of dimes: 10q

The total value is $1.60, so add the above value, set equal to 160 cents, and solve:

1q + 5q + 10q = 160

16q = 160

q = 10

There are 10 of each type of coin in the bag

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Practice problems involving coins

Problem 1:

John brings a pen and he gets change for $3 in 20 coins, all nickels and quarters. Find total numbers of each type are given?

Answer: john gets 10 nickels and 10 quarters.