SOLUTION: PurePets dog food is 35% vegetables 65% meat and grain. NewTone dog food is 42% vegetables and 58% meat and grain. How much of each would be needed to produce 25 pounds of dog food

Algebra ->  Graphs -> SOLUTION: PurePets dog food is 35% vegetables 65% meat and grain. NewTone dog food is 42% vegetables and 58% meat and grain. How much of each would be needed to produce 25 pounds of dog food      Log On


   

Question 977836: PurePets dog food is 35% vegetables 65% meat and grain. NewTone dog food is 42% vegetables and 58% meat and grain. How much of each would be needed to produce 25 pounds of dog food that was 50% vegetable and 50% meat and grain?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
p, how much of PurePets
n, how much of NewTone

n%2Bp=25 accounts for masses.

Accounting for vegetable:
%280.35p%2B0.42n%29%2F25=0.5
or
%2835p%2B42n%29%2F25=50

Accounting for meat:
%2865p%2B58n%29%2F25=50

Only two equations are needed for the system because only two unknown variables need resolution. A full system is

system%2835p%2B42n=25%2A50%2C65p%2B58n=25%2A50%2Cn%2Bp=25%29

and then

system%2835p%2B42n=1250%2C65p%2B58n=1250%2Cn%2Bp=25%29
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Best would be to omit either of the percentage equations, and use the mass equation to substitute for either n or p.