Question #93e34

1 Answer
Jul 10, 2016

Answer:

cashews#=35# lb
hazelnuts #=15# lb

Explanation:

Since we are required to find two quantities, we have two unknowns and need to formulate two equations.

Let us mix with 50 lbs of peanuts cashews #=x# lb
And let us mix with 50 lbs of peanuts hazelnuts#=y# lb
Total mixture#=100# lb

This gives us first equation
#x+y+50=100#
#x+y=50# .....(1)

Cost of #x# lb of cashews#=3.00xx x=3x#
Cost of #y# lb of hazelnuts#=2.50xx y=2.5y#
Cost of 50 lbs of peanuts#=1.75xx50=87.5#
Total cost of mixture#=3x+2.5y+87.5#
Per lb cost of mixture gives us the second equation
#(3x+2.5y+87.5)/100=2.30#
To eliminate decimals multiplying both sides by #1000# we get

#30x+25y+875=2300#
#=>30x+25y=1425# .......(2)

To solve the set of equation. From (1) we obtain
#x=50-y#,
inserting in (2) we get
#30(50-y)+25y=1425#
#1500-30y+25y=1425#
#-5y=-75#
#=>y=15#
This gives us
#x=50-y=50-15=35#