Question

A store sells cashews for 4.90 dollars per pound and peanuts for 1.30 dollars per pound. The manager decides to mix 10 pounds of peanuts with some cashews and sell the mixture for 2.90 dollars per pound. How many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

Answer 1

let x = pounds of cashews in the mix
pounds of peanuts in the mix equals 10
let y = pounds of the total mix

set up a system of two equations

1. (x lbs)(4.90 $/lb) + (10 lbs)(1.30 $/lb) = (y lbs)(2.90 $/lb)
2. x lbs + 10 lbs = y lbs

substitute in x + 10 from the second equation into the first

1. (x lbs)(4.90 $/lb) + (10 lbs)(1.30 $/lb) = (x lbs + 10 lbs)(2.90 $/lb)

distribute and solve

4.9x + 13 = 2.9x + 29
2x = 16
x = 8 lbs of cashews in the mix

Answer 2

understooD! thank u very much