SOLUTION: Macadamia nuts cost $.90 per ounce, peanuts cost $.30 per ounce, an cashews cost $1.30 per ounce. You want a 20- ounce mixture of macadamia nuts, peanuts, and cashews that costs $.

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Question 390126: Macadamia nuts cost $.90 per ounce, peanuts cost $.30 per ounce, an cashews cost $1.30 per ounce. You want a 20- ounce mixture of macadamia nuts, peanuts, and cashews that costs $.68 per ounce. If the combined weight of the macadamia nuts and cashews equals the wight of the peanuts, how many ounces of each nut should be used?
Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of peanuts
y=amount of macadamia nuts
z=amount of cashews
x+y+z=20----------------------------------eq1
0.30x+0.90y+1.30z=20*0.68=13.6---------------eq2
y+z=x--------------------------------------eq3
substitute y+z=x into eq1 and we get
2x=20
x=10 oz-------------------------amount of peanuts needed
substitute x=10 into eq2 and eq3 and we get:
0.90y+1.30z=10.6----eq2a
y+z=10-----eq3a
multiply eq3a by 0.90 and then subtract eq 3a from eq2a and we get:
0.40z=1.6
z=4 oz---------------------amount of cashews needed
substitute z=4 into eq 3a and we get:
y=6 oz--------------------------amount of macadamias needed
CK
0.30*10+0.90*6+1.30*4=13.6
3+5.4+5.2=13.6
13.6=13.6
Hope this helps---ptaylor