Need with this one also . due in half hour. greatly appreciate it

the total value of quarters and nickles in a jar full of change is $5.95. if the nickles were quarters and the quarters were nickles, the total value of the coins would be $3.35. find the number of nickles in the bank.

  9 nickels

Step-by-step explanation:

Changing a quarter to a nickel decreases the value of the sum by $0.20.

When all quarters are changed to nickels and vice versa, the total value will change by the number of excess quarters. That number is ...

  ($5.95 -3.35)/(0.20) = 2.60/0.20 = 13

The remaining change is made up of equal numbers of nickels and quarters. That amount of change is ...

  $5.95 -13·0.25 = 2.70

A quarter and nickel together total $0.30, so there must be $2.70/$0.30 = 9 such pairs of coins.

There are 9 nickels and 22 quarters.

If you don't want to reason through the problem, you can write equations. Let n and q represent the numbers of nickels and quarters, respectively. Then you have ...

  0.05n + 0.25q = 5.95

  0.25n + 0.05q = 3.35

Multiplying the second equation by 5 and subtracting the first gives ...

  5(0.25n +0.05q) -(0.05n +0.25q) = 5(3.35) -(5.95)

  1.20n = 10.80

  10.80/1.20 = n = 9

The number of nickels is 9.