How do you solve this problem. Please show steps. NOT THE ACTUAL ANSWER.?

C = cashew @ $5/lb

P = peanuts @ $1.50/lb

T = target @ $4/lb

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the ratio of C & P needed will be in inverse proportion to distance from T

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C:P = (4 - 1.5) : (5 - 4) = 2.5:1 = 5:2

cashews needed = (5/7)*32 lbs

peanuts needed = (2/7)*32 lbs

work it out !

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p.s.

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if your teacher insists on an algebraic solution,

let there be C lbs of cashewnuts, so (32-C) lbs of peanuts, &

5C + 1.5(32-C) = 4*32

solve !

Let C = number of pounds of cashews and P = number of pounds of peanuts

C + P = 32

5C + 1.5P = 4(32) (this is the total cost of the 32 pounds)

so multiply the first equation by 5:

5C + 5P = 160

5C +1.5P = 128

subtract:

3.5P = 48

P = 48/3.5 = 13 5/7 lbs

C = 32 - 13 5/7 = 18 2/7 lbs

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let x=pounds of cashews

let y=pounds of peanuts

x+y=32

5x+1.5y=32*4

solve the system of equations by either substitution or elimination

x=32-y

5(32-y)+1.5y=128

160-5y+1.5y=128

32=3.5y

32/3.5=y

9.1 ≈ y

x=32-9.1

x=22.9