Posted by Sandra on Wednesday, October 17, 2012 at 12:02am.
If paint is sold for $ 15 a can and $20 a can and they sell 320 dollars worth of paint, how many cans of paint do they sell? I know it takes 7 cans of paint at 20 equaling 140 and 12 cans at 15 equaling 180 but I', stumped at how to write the equation

math  Anonymous, Wednesday, October 17, 2012 at 12:35am
Let x = 15$ paint

math  Reiny, Wednesday, October 17, 2012 at 9:17am
Number of $15 cans  x
number of $20 cans  y
15x + 20y = 320
divide by 5
3x + 4y = 64
we are looking at the equation of a straight line, where the solutions can only be integers, (can't buy a partial can of paint)
xintercept = 64/3 , x < 21
yintercept = 64/4 , y < 16
3x = 644y
x = (644y)/3
644y must be a multiple of 3
with y as an integer, 644y can only be
60 56 52 48 44 40 36 32 28 24 20 16 12 8 4
of those the only multiples of 3 are:
60 48 36 24 and 12
so, assuming they buy at least one of each can, possible solutions for (x,y) are
(20,1)
(16,4)
(12,7)  your answer
(8,10)
(4,13)