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Mathematics
OpenStudy (anonymous):

Tim and Judy mix two kinds of feed for pedigreed dogs. they wish to make 28 pounds of feed worth $0.19 per pound by mixing one kind worth $0.13 per pound with another worth $0.29 per pound. How many pounds of the cheaper kind should they use in the mix?

OpenStudy (sandra):

ok, so from the problem we know after mixing we want the average pound to be worth .19, and that the total number of pounds should be 28

OpenStudy (sandra):

so we have two unknowns, and hence we need two equations to solve this

OpenStudy (sandra):

so the first one is that (.13*x + .29*y)/28 = .19

OpenStudy (sandra):

that is the direct translation of "the average pound costs .19 after adding both components together")

OpenStudy (sandra):

now the second equation we know, is that when we add the two amounts together, there are a total of 28 pounds

OpenStudy (sandra):

i.e. x+y = 28

OpenStudy (sandra):

so now you have to use substitution to get either x or y

OpenStudy (sandra):

so let's take the second equation's value of "y", which is the more expensive amount, and substitute it back into the first equation

OpenStudy (sandra):

y = 28 - x

OpenStudy (sandra):

so if we put that back into the first equation, in place of y ("substituing"), we get: .13x + .29(28 -x) = .19

OpenStudy (sandra):

can you solve for x from there?

OpenStudy (sandra):

whoops sorry, above line should ready (.13x + .29(28-x))/28 = .19

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