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.