## A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of \$3.35. If the dimes were nickels, the nickels wer

Question

A collection of 20 coins made up of only nickels, dimes, and quarters has a total value of \$3.35. If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of \$2.75. How many quarters are in the original collection?

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1 week 2021-09-15T22:50:02+00:00 1 Answer 0

1. Answer:  The required number of quarters in the collection is 11.

Step-by-step explanation:  Given that a collection of 20 coins made up of only nickels, dimes and quarters has a total value of \$3.35.

If the dimes were nickels, the nickels were quarters and the quarters were dimes, the collection of coins would have a total value of \$2.75.

We are to find the number of quarters in the collection.

Let x, y and z represents the number of nickels, dimes and quarters respectively in the collection.

We will be using the following values of nickels, dimes and quarters in form of dollar :

1 nickel = \$ 0.05,   1 dime = \$ 0.10   and    1 quarter = \$0.25.

Then, according to the given information, we have Substituting the value of x from equation (i) in equations (ii) and (iii), we have and Comparing the values of y from equations (iv) and (v), we get Thus, the required number of quarters in the collection is 11.