Question 939904: A natural food store makes its own brand of trail mix out of dried apples, raisins, and peanuts. One pound of the mixture costs $3.18. It contains twice as much peanuts by weight as apples. One pound of dried apples cost $4.48, one pound of raisins $2.40, and one pound of peanuts $3.44. How many ounces of each ingredient are contained in one pound of the trail mix?
I have to use a 3x3 matrix to slove it but I can't figure out what the 3 equations would be
Answer by josgarithmetic(39616)   (Show Source):
You can put this solution on YOUR website! Do all as pounds and convert to ounces after solution of pounds is found.
Variables, a, r, p, for apples, raisins, peanuts
PRICES
Apples, 4.48
Raisins, 2.40
Peanuts, 3.44
Account for the price of mixture, $3.18/pound.
 ---not like this step
 , one of the equations for the system.
Peanuts and Apples relationship:
 , meaning  , another equation for the system.
How much mixture?
ONE pound.
 , now you have all the equations for the system.
Including coefficients of possible 0, or zero, and ordered first three columns as a, r, p, the system can be as this:
65a-39r+13p=0,2a-p=0,a+r+p=1
That negative sign in the first equation seems unexpected. I might have made a mistake in the work for that equation.
You can recheck, and then finish the solution process.
Notice also, the coefficients of the first equation are products of 13, so
|
|
|
