Answer:
20 pounds of peanuts and 80 pounds of cashews.
Step-by-step explanation:
A nut wholesaler sells a mix of peanuts and cashews.
We need to find the amount of peanuts and cashews should be used to make 100 pounds of the mix.
Let x pounds of peanuts y pounds of cashews are mixed.
[tex]x+y=100[/tex] .... (1)
He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If the mix is to sell for $4.80 per pound.
[tex]2.80x+5.30y=4.80\times 100[/tex]
[tex]2.80x+5.30y=480[/tex] .... (2)
From (1) we get
[tex]x=100-y[/tex] .... (3)
Substitute this value in equation (2).
[tex]2.80(100-y)+5.30y=480[/tex]
[tex]280-2.80y+5.30y=480[/tex]
[tex]2.50y=480-280[/tex]
[tex]2.50y=200[/tex]
Divide both sides by 2.50.
[tex]y=80[/tex]
Substitute y=80 in equation (3).
[tex]x=100-80=20[/tex]
Therefore, 20 pounds of peanuts and 80 pounds of cashews should be used to make 100 pounds of the mix.
