Word problem

Question

Benjamin has $7.40 in change, all in comes and quarters he has 44 in all. How many are dimes?

Answer 1

Hi Felicia,

 

Assume you had a typo "comes" instead of "dimes" as your question concerned the number of dimes.

 

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

    d = number of dimes

    q = number of quarters

 

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

    Equation #1 (based on number of coins):

        d + q = 44

    Equation #2 (based on value of coins):

        (0.10)(d) + (0.25q) = 7.40

 

Next, let's solve our two equations for our two unknowns:

    d + q = 44 (Equation #1)

          q = 44 - d (q in terms of d)

    (0.10)(d) + 0.25(q) = 7.40 (Equation #2)

    (0.10)(d) + (0.25)(44 - d) = 7.40 (q in terms of d)

    0.10d + 11.00 - 0.25d = 7.40

    0.25d - 0.10d = 11.00 - 7.40

    0.15d = 3.60

    d = 3.60/0.15

    d = 24 dimes

    q = 44 - d (q in terms of d)

    q = 44 - 24

    q = 20 quarters

 

Finally, we can verify our answers by plugging them back into Equation #2 and check to see that the sum of the coin amounts equals the total change amount:

    (0.10)(d) + (0.25)(q) = 7.40 (Equation #2)

    (0.10)(24) + (0.25)(20) = 7.40

    2.40 + 5.00 = 7.40

    7.40 = 7.40 (coin amounts = total amount)

 

Since the sum of both coin amounts is equal to the total change amount, we are confident that our answers for the numbers of each coin denomination are correct.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.