Results 1 to 4 of 4

Thread: Help w/ word problem regarding coin quantities: Jessica has 16 dimes and quarters.

  1. #1

    Help w/ word problem regarding coin quantities: Jessica has 16 dimes and quarters.

    The problem is this:

    Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica. If they both have the same amount of money, what coins does each have?

    I've tried using a chart and systems of equations to solve but can't figure it out. The solution is this:

    Jessica has 10 dimes and 6 quarters
    Whitney has 20 dimes and 2 quarters

    Can someone show me the proper steps to arriving at this solution? Thanks!

  2. #2
    Elite Member mmm4444bot's Avatar
    Join Date
    Oct 2005
    Location
    Seattle
    Posts
    9,429
    Quote Originally Posted by seattledude View Post
    Jessica has 16 dimes and quarters. Whitney has twice as many dimes and 1/3 as many quarters as Jessica. If they both have the same amount of money, what coins does each have?

    I've tried using a chart and systems of equations to solve but can't figure it out
    Hi. Please show us the equations that you came up with, even if you think they are wrong. Sometimes, when a student reads a statement like, "Whitney has twice as many dimes as Jessica", they put the factor 2 on the wrong side of the equation (common mistake). We'd like to check over what you've tried so far. Maybe it's just a simple mistake, somewhere.

    Please also be sure to read the forum's guidelines. Thanks.
    Last edited by mmm4444bot; 01-28-2018 at 11:45 PM. Reason: added: "factor"
    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  3. #3
    So, here was my original approach

    Let d represent the quantity of dimes.
    Let q represent the quantity of quarters.

    Jessica: d + q = 16
    Whitney: 2d + 1/3q = ?

    We know that both people have the same amount of money. Consequently,

    d + q = 2d + 1/3q

    Given that we have d + q = 16, I transformed the equation like so: q = 16 - d. Next, I swapped instances of q for 16 - d like so:

    d + (16-d) = 2d + 1/3(16-d)

    This did not yield the results I expected. Looking for a correct approach. Thanks.

  4. #4
    Senior Member
    Join Date
    Nov 2017
    Location
    Rochester, NY
    Posts
    1,590
    Quote Originally Posted by seattledude View Post
    So, here was my original approach

    Let d represent the quantity of dimes.
    Let q represent the quantity of quarters.

    Jessica: d + q = 16
    Whitney: 2d + 1/3q = ?

    We know that both people have the same amount of money. Consequently,

    d + q = 2d + 1/3q

    Given that we have d + q = 16, I transformed the equation like so: q = 16 - d. Next, I swapped instances of q for 16 - d like so:

    d + (16-d) = 2d + 1/3(16-d)

    This did not yield the results I expected. Looking for a correct approach. Thanks.
    You actually have a good start. We can work with it.

    You've defined (without explicitly stating it, which is an important thing to do):
    d = number of dimes Jessica has
    q = number of quarters Jessica has

    Then you correctly wrote an equation saying Jessica has 16 coins: d + q = 16.

    You also wrote an expression for the number of coins Whitney has: 2d + 1/3q. This depends on the facts
    2d = number of dimes Whitney has
    (1/3)q = number of quarters Whitney has

    These are correct facts. But we don't know anything about the number of coins Whitney has; what we know is that they both have the same AMOUNT OF MONEY -- that is, the same VALUE.

    Write an expression for the VALUE of each one's coins, and set those expressions equal. That will give you the second equation you need.

Tags for this Thread

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •