SOLUTION: A grocer mixed nuts worth $4 per kilograms with raisins worth $3.25 per kilogram to make 15 kg of a mixture worth $3.69 per kilogram. How many kilograms of nuts were used ?

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Question 720539: A grocer mixed nuts worth $4 per kilograms with raisins worth $3.25 per kilogram to make 15 kg of a mixture worth $3.69 per kilogram. How many kilograms of nuts were used ?
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
An item at a price H was mixed with an item at price L to make M quantity of mixture worth T. How much of each item was used?

Let u = amount of lower priced item to use
Let v = amount of higher proced item to use

highlight%28%28Lu%2BHv%29%2FM=T%29 and highlight%28u%2Bv=M%29. Solve for and find u and v.

From rational equation, Lu%2BHv=TM. Using the M sum equation, v=M-u.
Lu%2BH%28M-u%29=TM
Lu%2BHM-Hu=TM
Lu-Hu=TM-HM
%28L-H%29u=%28T-H%29M
u=%28T-H%29M%2F%28L-H%29, and because T-H and L-H are both negative, multiplication by %28-1%29%2F%28-1%29 gives us:
highlight%28u=%28H-T%29M%2F%28H-L%29%29.

You can continue onward to solve for v, and then substitute given values to compute u and v.