Gaby's piggy bank contains quarters and nickels worth ​$13.60. If she has 84 coins in​ all, how many of each does she​ have?

Answer 1

If a piggy bank contains quarters and nickels worth $13.60, we can model that as 0.25q + 0.05n = $13.60 where q is the number of quarters and n is the number of nickels. Furthermore, if there are 84 coins in all, we can model that as q + n = 84. Thus we have 2 equations and 2 unknowns which we can solve simultaneously via elimination.

If we choose to eliminate q then we can multiply the second equation by -0.25 and it becomes

-0.25q - 0.25n = -21. We then add the new 2nd equation to the first equation to eliminate q and we get

-0.2n = -7.40 --------> n = 37 or 37 nickels. Subtract 37 nickels from the 84 total coins to find number of quarters, 84 - 37 = 47 quarters