School-Safe Puzzle Games

Mother Thrifty & Daughter Dollie

Mother Thrifty and her daughter Dollie each drive 30 ducks to the market. Mother Thrifty is eager for a trade, and hurries on with her 30, and reaches the market early when ducks are in demand. She sells two for one dollar; but Dollie dawdles along the road, and when she arrives the market is supplied so she only receives one dollar for every three.

On the way home the mother says, "I got a dollar for two, and you a dollar for three, which makes two dollars for five ducks; but sixty is twelve times five, so we must have twelve times two dollars or twenty-four," but on counting their money they found they had twenty-five dollars.

Why this discrepancy?


11 Comments to “Mother Thrifty & Daughter Dollie”

  1. jasc | Profile

    mother’s calculations assume:
    24 sold at 2/ $1
    36 sold at 3 /$1

    actually 30 at each rate

  2. tumeke | Profile

    Can only add fractions with common denominators.
    Mother Thrifty and Daughter Dollie were selling ducks at different rates.

    30/ 2 =15 (Thrifty_at 2 ducks per dollar)
    30/ 3 =10 (Dollie_at 3 ducks per dollar)

    15+10 =25

  3. Tommy | Profile

    Mother has 15 groups of 2, and daughter has 10 groups of 3. That would be 10 groups of $2 for 5 and 5 groups of two. Basically, mother has more groups of two than daughter has groups of 3.

  4. Shawn | PUZZLE GRANDMASTER | Profile

    The IRS will be watching this family for tax evasion via under-reporting in the months to come.

    This is a problem of rates, not of static numbers as old Mother Thrifty mistakenly assumes.

    The math must be set up as:

    x = 3 ducks / $1
    y = 2 ducks / $1

    Mommy sold at rate y.
    Dollie sold at rate x.

    The rates are different, and so are not additive.

    Mommy is correct in the ratio $2 / 5 ducks sold, but only as long as both Mommy and Dollie have enough ducks to continue to sell together at their respective rates.

    If Mommy and Dollie actually sold their ducks together at the same time but at their respective rates, Dollie would run out of ducks after ten sales (10 sales * 3 ducks / $1 = 30 ducks sold). After ten sales, Mommy would still have 10 ducks to sell (10 sales * 2 ducks / $1 = 20 ducks sold). These would be sold at the rate of 2 ducks/$1, yielding an additional $5. Added to the $20 already earned (10 sales * (5 ducks/sale) * ($2/5 ducks) gives a total of $25 for the family.

    Mother Thrifty is to be commended for her market knowledge and her grasp of the supply & demand concept, but should probably leave the book-keeping to Dollie.

  5. suineg | PUZZLE MASTER | Profile

    ok, the explanation why is 25 $ is this:
    Mother: 30 ducks in groups of two –> 15 groups at 1 $ each= 15 $
    Daugther: 30 ducks in groups of three–> 10 groups at 1$ each= 10 $
    the sum is 25$

    Now why is that discrepancy, i think is because there are 12 groups of 5 ,
    but in the reality when you mix the are 10 groups of 5 and 5 groups of 2 of the mother that does not mix, 10 of 5 are 20 $ and 5 of 1$ of the mother are 5$ , the sum again 25$.

    the wrong thing with the 5–>12 groups is that the 5 groups of two remains entirely of the mother getting the advantage of the market relationship of going early when yo mix you lose that advantage because yo turn 5 groups of two ducks that are from the mother in two groups of 5 ducks, the first represent 5 $ the second 4 $ so getting the 1 $ difference.
    I hope that with this I get my reivindication jajajajajajaja, just kidding, nothing would bounce me back of a stunning middle school failure.

  6. Carpenter | Profile

    30*1/2 + 30 *1/3 = 30(1/2+1/3) = 30(5/6) = 25

    The statement “I got a dollar for two, and you a dollar for three, which makes two dollars for five ducks” is only valid if for every 2 ducks Mother Thrifty sells, Dollie sells 3 ducks. However, this is not true, as they each sold 30.

  7. T | Profile

    It’s a matter of how the addition was done… it was $1 for 2 ducks and $1 for 3 ducks not $2 for 5. I don’t know the logical reasoning but the mathematical reasoning is like this:

    30 / 2 + 30 / 3 = ((3*30)+(2*30)/6) = 150/6

    Or order of operations, you have to do the division before you can do the addition.

    so the answer is not 60/5 * 2 = 24 but actually 30/2 * 1 = 15 and 30/3 * 1 = 10 means total $ = $25

  8. Gray-T | Profile

    I am glad that creativity in my business is more important than math.
    :-) You guys are really awesome at this kind of things !


  9. suineg | PUZZLE MASTER | Profile

    Cool Gray-T, “Imagination is more important than knowledge” or something like that said Einstein long before.

    But even in maths I think creativity is realy important. Greetings : >;)
    My mojo is taken from Twain i think it says ” I never let schooling interfiere with my education” jajaja but maybe thats working againt me.

  10. sebbie3000 | Profile

    I like this site, but why do the answers have to be so complicated. I worked this one out like this:

    They cannot be added up that way, as the rates are different. Therefore the simplest way to the correct answer is:
    30/2 = 15 (the amount Thrifty gained)
    30/3 = 10 (the amount Dollie gained)
    Add both amounts = 25.

    There, simple and doesn’t take half an hour to write!

  11. lil_b7717 | Profile

    they have $25 because the mom sold hers 2 for $1 (30/2=15; 15*1=15) and the daughter sold hers 3 for $1 (30/3=10; 10*1=13) so their total equals up to $25 (15+10=25)

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