A piggy bank contains 50 coins, all of them nickels, dimes, or quarters. The total value of the coins is $5.60, and the value of the dimes is five times the....

Question

A piggy bank contains 50 coins, all of them nickels, dimes, or quarters. The total value of the coins is $5.60, and the value of the dimes is five times the Value of the nickels. How many coins of each type are there? 

Answer 1

There are three equations to be solved.  N-nickels, D-dimes, Q-quarters.  N + D + Q = 50 [the quantity of coins].  5N + 10D + 25Q = 560 [total value].  5x (5N) [value of nickels] = 10D [value of dimes].  Now solve the third equation for N and substitute the answer in the first equation and Solve for D then repeat for Q in the second equation.  

It also helps to envision a simple answer such as:   all dimes but one quarter and one nickel.  That would be 48 X 10 [dimes] and 25 [quarter] and 5 [nickel] which equals 510 which is close.  So now you know you need a couple more quarters (for more value).