Buying Flowers
Knightmare decides to buy his couch some flowers for Valentines Day ... (hmmm ... must be the little voices he hears ... oh well). Thinking it is tea, he accidentally consumes a large quantity of bourbon ... then heads to the florist.
He buys x number of flowers for y dollars (x and y are integers). As he staggers ... ooops, I mean walks away from the counter, after paying, the clerk says "If you buy ten more flowers, I will give you all for $2.00, and you will save $.80 a dozen". (the little voice says "don't do it").
How many flowers will Knightmare present to his lovely couch on Valentines Day? ... and how much did he spend?
He buys x number of flowers for y dollars (x and y are integers). As he staggers ... ooops, I mean walks away from the counter, after paying, the clerk says "If you buy ten more flowers, I will give you all for $2.00, and you will save $.80 a dozen". (the little voice says "don't do it").
How many flowers will Knightmare present to his lovely couch on Valentines Day? ... and how much did he spend?
posted by Zaux at
6:52 AM
8 Comments:
i would say he bought 60 flowers for $124
He bought 50 flowers @ $3.2/dz. Makes it $160 in total
but that can't make sense..
with 10 more flowers he would had 60 and because 1 would cost $2 then the total price would be $120, which is less than for 50 flowers, so the seller must be very stupid
he bought one dozen for $2.00 instead of one dozen @ $3.20 (he had 2 flowers plus the ten to make it one dozen @ $3.20 - the .80 cent discount for total of 1 dozen for $2.00
To me it seems that the shopkeeper means that he will give him the rest of 10 for $2.
Reducing overall price will obviously get him cheaper, no matter what numbers you put in. The numbers are a way of making calculations back to the original price so:
10 flowers = $2 + $.80 (before discount)
Hence rate = $3.2/dozen
Also the number of flowers + 10 must be divisible by 12 and the total cost must be integral.
A bit of maths tells me that such a number is 50 since (50 + 10)/12 = 5 and also 5 * 3.2 is a round number. There can be other solutions as well but this is the least number according to my calculations.
i meant 2.80 instead of 3.20
Hi Zulfiqar ...
you are right ... he bought 5 flowers
Since y is an integer < 2, y = 1. Then, dealing with price per flower in cents,
100/x + 200/(x+10) = 80/12 or
x^2+25x-150=0
of which the positive root is x=5, the number of flowers originally purchased.
oops ... error above
should be:
100/x - 200/(x+10)= 80/12
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