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Ned, the owner of Ned's Nut Shop, sells peanuts for $10 per pound and cashews for $9 per pound. Ned wants tocreate a 20 pound barrel of mixed nuts and sell it for $9.70 per pound. How many pounds of peanuts andcashews should Ned use?Ned should mix 9 pounds of peanuts and 11 pounds of cashews to make 20 pounds of a blend that sells for$9.70 per pound.

Respuesta :

let peanuts be p

and cashews be c

Since he wants a total of 20 pound, so we can write:

[tex]p+c=20[/tex]

Peanut cost 10 and cashews cost 9 (per pound) and total 20 pounds cost 9.70*20 = 194 dollars, thus we can write:

[tex]10p+9c=194[/tex]

Rearranging the first equation, we have:

[tex]\begin{gathered} p+c=20 \\ p=20-c \end{gathered}[/tex]

Plug this into 2nd equation and solving for c gives us:

[tex]\begin{gathered} 10p+9c=194 \\ 10(20-c)+9c=194 \\ 200-10c+9c=194 \\ 200-194=10c-9c \\ 6=c \end{gathered}[/tex]

Since we know p = 20 -c, so

p = 20 - 6 = 14

So, the mixture should be:

14 pounds peanuts, and

6 pounds of cashews

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