Acollection 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?

 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.

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