Math Help please, intermediate difficulty

[webnewland]

a girl entered a store and bought X flowers for Y dollar ( X and Y are integers) when she was leaving, the clerk said " if you buy 10 more flowers, i will give you all for $2 and you will save 80 cents a dozen, FIND X AND Y

I found the formula Y - { ((x+10)/12) * 0.8 } = 2

but not sure what to do next
thx for the help

 

[ErmanC]

Problem seems to be indeterminant even with the integer caviat thrown in.
Let X = # flowers, A = Unit price without discount, B = unit price with discount, Y = cost without discount

X A = Y
(X+10) B = 2
12 A = 12 B - .8

3 equations and 4 unknowns so the solution set is indeterminant.

 

[klah]

Originally posted by: webnewland
a girl entered a store and bought X flowers for Y dollar ( X and Y are integers)

Is that $Y/each or is Y the total cost?

 

[webnewland]

Y is the total amount (before discount, the actual amount she paid)

 

[bizmark]

It can be solved with a little more thought....

so it's unsolvable normally, but think about it... the original dollar amount is an integer. It's got to be less than 2. And it must be greater than 0 since otherwise she'd be getting the flowers for free, and she wouldn't be getting an 80-cent discount per dozen when she's actually paying $2 for some flowers and she originally was going to pay nothing for some flowers. What's the only integer between 0 and 2? 1, of course. So she spent a dollar to buy a certain number of flowers. I started plugging in numbers, then I got lazy so I just made a small spreadsheet.... I ended up with 5 as the answer. Check it out:

5 flowers for $1 => $2.40 per dozen
15 flowers for $2 => $1.60 per dozen
= 80-cent savings per dozen.

my spreadsheet (you'll have to reconstruct it yourself since the forum won't allow me to format with tabs):

(orig. #) (orig. price/doz) (new #) (new price/doz) (price difference / doz)
10.00 1.20 20.00 1.20 0.00
9.00 1.33 19.00 1.26 0.07
8.00 1.50 18.00 1.33 0.17
7.00 1.71 17.00 1.41 0.30
6.00 2.00 16.00 1.50 0.50
5.00 2.40 15.00 1.60 0.80
4.00 3.00 14.00 1.71 1.29
3.00 4.00 13.00 1.85 2.15
2.00 6.00 12.00 2.00 4.00
1.00 12.00 11.00 2.18 9.82

edit: clarification
edit2: parentheses around the column headings

 

[RossGr]

It can also be solved with straight forward algebra. Useing the same logic as above, if she paid a total of $2 for all the roses, she must have initially spent $1. so 1$ for x roses means she paid

12/x per doz the deal was to get 10 more roses for $2 so she then paid

24/((x+10) per doz we now can write an equation

(12/x) -.8 = 24/(x+10)

This leads to a quadratic

x^2 +25x -150 =0

which factors to
(x+30)(x-5)=0

take the postitive root to get x=5 , the same result as above.

 

[silverpig]

Leave it to Ross to solve the math problem

 

[bizmark]

nice. I didn't even think to try making an equation I knew that I was restricted to only a few choices (i.e. 10 or less) so I just decided to plug in numbers until I got the right one.