The total value of the quarters and dimes in a coin bank is $6.90. If the quarters were dimes and the dimes were quarters, the total value of the coins would b

Question

a) Set up a system of equations to represent the situation.

b) Find the number of quarters in the bank.

Answer 1

Here is how you set it up but the final value of the reverse coins didn't come through so I can't show you a complete solution.

 

let q = #of quarters

let d = # of dimes

 

multiply q and d by the respective quantities for the values of the coins and sum them to equal the amount in the bank. Then switch the coins and their values to represent the second equation. Now you have two systems of equations and you proceed normally. Pick one value q or d make them equal but opposite so they cancel and then solve for the remaining variable. Plug the solved variable into one of the equations to find the remaining unknown.

 

25q +10d = 690

10q + 25d =  ?