SOLUTION: raisins cost $7 per pound and peanuts cost $3 per pound. How many pounds of each should you use to make a 10 pound mixture that cost $5.40 per pound

Question 813212: raisins cost $7 per pound and peanuts cost $3 per pound. How many pounds of each should you use to make a 10 pound mixture that cost $5.40 per pound
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
x and y for raisins and peanuts, their poundages.

and
Two equations in two unknowns. Tell me if you need help with the steps from these equations.

----Help Requested:

Try to at least partially simplify the rational equation.

Various ways to go from here. One method can be use the second equation solved for y and substitute into the "54" equation.
, so use this to form...

And use that to solve for x. Once done, use the second simpler equation, the , to finish solving for y.

ANOTHER APPROACH to the Simultaneous Equations.
-----------------------------------------------
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Again, partially simplifying the rational equation into 7x+3y=54;
and using the x+y=10,
we have the system:
---------------------------

----------

---------------------------

Try elimination of one variable and solve for the other. The most obvious way is to multiply the "10", second equation by 3, and subtract the result from the "54" equation, like so:
------->
and then,

pounds of raisins
'
Use the x+y=10 equation now to find value of y.

pounds of peanuts

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