Question

At the craft store, a paint brush costs $0.79, and a small bottle of paint costs $0.89. What combination of paint brushes and bottles of paint could you buy for exactly $4.15?
(No tax included. NOT A TAX PROBLEM.)

Answer 1

this looks like a guess and check problem to me

Answer 2

\(1\times .79+4\times .89=4.35\) nope
lets try again

Answer 3

\(2\times .79+3\times .89=4.25\) ok not that one either

Answer 4

bet we get it on the next try though...

Answer 5

oh yeah, next one works

Answer 6

hello any1? i waited for like one hour and a half already -_-

Answer 7

did you not understand my answer?

Answer 8

maybe it was not clear. method is to guess and check to see if it works
started with one paint brush and four bottles , got a total cost of
\[1\times .79+4\times .89=4.35\] which is too big,
then tried 2 paint brushes and 3 bottle for a total cost of
\[2\times .79+3\times .89=4.25\] again too big
so what would the next one in this list be?

Answer 9

i actually don't know because there are unlimited answers

Answer 10

did you try the next one?

Answer 11

i didn't because my point is, there are unlimited numbers to plug into the equation

Answer 12

that is i suppose technically true, that is you could try any number of brushes and paint, but not any will add to $4.15

Answer 13

for example one million of each would be silly

Answer 14

yes that would be my point, but it would be unlimited money LOL :P yes that's my point, but what i'm trying to say is, you can do 5 or 6 or 7 or 8 or 9 or 10 or 11 or 12 or 13 or 14 or 15 and so on and so forth

Answer 15

i understand that you have only one equation and two unknowns, and so if the number of brushes and the number of cans could be any number at all, then you would have an infinite number of solutions to \(.79x+.89y=4.15\)

Answer 16

but in this case \(x\) and \(y) must be whole numbers, not any number

Answer 17

There isn't an unlimited number of answers because there's only a few combinations that won't exceed $4.15 and x and y must be whole numbers.

Answer 18

and of course in your examples above, none of the work because they add up to more than $4.15

Answer 19

an equation with only integer solutions goes by the fancy name of "diophantine" equations
you are asked here for whole number solutions, and the way to find them is, well, to find them
guess and check, see what works

Answer 20

so do i use the equation 0.79x +0.89y=4.15?