The manager of a coffee shop has one type of coffee that sells for $5 per pound and another type that sells for $12 per pound. the manager wishes to mix 90 pounds of the $12 coffee to get a mixture that will sell for $10 per pound. How many pounds of the $5 coffee should be used?
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Plz some one help me i have been trying to work this problem forever!!!
so call x the number of pounds of $5 coffee and y the number of pounds of $12 coffee
you know that they want x + y = 90
and so you have to figure 5x + 12y = 900
why 900? because they want 90 lbs and for the mix to sell for $10 a pound
the way to do this is by substitution or elimination
we can do substitution. so use the first equation and we get y = 90 - x (by subtracting x from both sides)
then using this lets substitute into the second to get
5x + 12(90 - x) = 900
then doing some algebra we get
5x + 1080 - 12x = 900
getting the variable on one side we get 180 = 7x
solve for x we get 180/7
then back substitute into the first equation we get 180/7 + y = 90 and then you get y = 450/7