How many quarters and nickels does Joe have?

Question

In his coin bank, Joe has 3 times as many quarters as nickels. The value of quarters is $5.60 more than the value of nickels. How many of each kind does he have?

Answer 1

Hi Bianca,

 

Let's begin by assigning letters to represent our two unknowns:

    q = # of quarters

    n = # of nickels

 

Next, let's write two equations we can use to solve for our two unknowns:

    Equation #1 (3 times as many quarters as nickels):

        q = 3n

    Equation #2 (total value of quarters is $5.60 more

                       than total value of nickels):

        (0.25)q = (0.05)n + 5.60

 

Now we'll group our equations and solve for our two unknown:

    q = 3n                             [equation #1]

    (0.25)q = (0.05)n + 5.60    [equation #2]

    (0.25)3n = (0.05)n + 5.60  [replace q with 3n]

    0.75n = 0.05n + 5.60

    0.75n - 0.05n = 5.60

    0.70n = 5.60

    n = 8 (# of nickels)

    q = 3n    [equation #1]

    q = 3(8)  [n = 8]

    q = 24 (# of quarters)

 

Finally, we can verify our answers by plugging them back into Equation #2 to see if both sides balance:

    (0.25)q = (0.05)n + 5.60        [equation #2]

    (0.25)(24) = (0.05)(8) + 5.60  [answer plug-ins]

    6.00 = 0.40 + 5.60

    6.00 = 6.00 (both sides balance)

 

Since both sides balance, we are confident that our answers are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.