Question

Question #93e34

Answer 1

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`