A nut mixture of walnuts and cashew nuts at a small fair is $1.00 per pound of walnuts and $4.19 per pound of cashew nuts. Over the entire day, 121 pounds of the nut mixture were sold for $280.50. If p is the number walnuts and n is the number of cashew nuts, then the system of equations that models this scenario is: p+n=121p+4.19n=280.50

50 pounds of cashews and 71 pounds of walnuts were sold.

Our system of equations is
p+n = 121
p+4.19n = 280.50

Since the coefficients of p are the same, we will begin solving this by subtracting the second equation from the first:

[tex] \left \{ {{p+n=121} \atop {-(p+4.19n=280.50)}} \right. \\ \\-3.19n = -159.50[/tex]

Divide both sides by -3.19:
-3.19n/-3.19 = -159.50/-3.19
n = 50

There were 50 pounds of cashews sold.

To find the value of p, the pounds of walnuts, substitute 50 in for n in the first equation:
p+n = 121
p+50 = 121

Subtract 50 from both sides:
p+50-50 = 121-50
p=71

71 pounds of walnuts were sold.