SOLUTION: in what ratio must tea costing P24 per kg be mixed with tea costing P34 per kg so that a profit of 20% is made by selling the mixture at P36 per kg?

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Question 763032: in what ratio must tea costing P24 per kg be mixed with tea costing P34 per kg so that a profit of 20% is made by selling the mixture at P36 per kg?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
What would be the price of the mixture of these teas, if u= kg of P24 type and v = kg of the P34 type:
24u%2B34v P units for %28u%2Bv%29 kilograms.
The 1 kg unit cost is %2824u%2B34v%29%2F%28u%2Bv%29 P per kg.

Undo that 20% profit to know the cost per kg for the mixture originally.
%281%2F1.20%29%2836%29=30 P per kg is this original mixture price or cost.

Original mixture price: %2824u%2B34v%29%2F%28u%2Bv%29=30
And we could have assumed the original mixing were based on forming a 1 kilogram mixture, so that u%2Bv=1

Use that sum relationship as substitution to the "30" equation and divide left & right by 2 to simplify that "30" so you have this system to solve:
%2812u%2B17v%29%2F1=30 and u%2Bv=1
highlight%2812u%2B17v=30%29 and highlight%28u%2Bv=1%29
Now just solve for u and v.