algebra

A coffee merchant has coffee beans that sell for $9 per pound and $12 per pound. The two types are to be mixed to create 100 lb of a mixture that will sell for $11.25 per pound. How much of each type of bean should be used in the mixture?

I am trying to figure the equation for this problem

would the equation be 9x+12y=100
if it is where do i go from there

You need 2 different equations.

x = amount (in pounds) of $9 coffee
y = amount (in pounds) of $12 coffee

x + y = 100 lbs all together.

As far as the cost goes:
($9x + $12y)/100 = $11.25

When you have 2 equations like that, you want to get one of the variables by itself in one of them. Let's take the top equation and get "x" by itself.

x=100-y

Now you know how much "x" is worth. Plug it into the 2nd equation. Our second equation looked like this:
(9x + 12y)/100 = $11.25

It will be easier to, right now, multiply both sides by 100 to get rid of the fraction.
9x+12y = 1125

Now, plug in what you know for "x" and you get:

9(100-y) + 12y = 1125
Multiply out the 9:

900-9y+12y = 1125

Now, solve for "y"
900+3y = 1125
3y = 225
y=75

So you need 75 lbs of the $12 one and (since it's 100 lbs between the 2 of them...and 75 + 25 = 100)... 25 lbs of the $9 one.

Let's double check:

$75*12 + $9*25 = $1125

$1125 / 100 lbs = $11.25 per pound

Sweet. Just did that as I went and it worked out. Sometimes, I get all the way through and realize I made a mistake and have to go back and try it again. That would have been a lot of typing to redo :)

You're welcome :)

Thank you so much this explains alot to me on some of my other problems i have been having trouble with i think i can fix them now thank again

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