A nut mixture of peanuts and pecans at a small fair is $1.00 per pound of peanuts and $4.25 per pound of pecans. Over the entire day, 115 pounds of the nut mixture were sold for $358.75. If p is the number peanuts and n is the number of pecans, then the system of equations that models this scenario is:

since p = 115-n, use that to get

115-n + 4.25n = 358.75
now find n, then p

HUH???

oh, please.

115-n + 4.25n = 358.75
3.25n = 243.75
n = 75
so p = 115-75 = 40

you need to review solving systems of equations, yeah?

To determine the amount of peanuts and pecans that were sold, we need to solve the system of equations:

1) p + n = 115
2) p + 4.25n = 358.75

We can solve this system of equations using either substitution or elimination method. I will use the elimination method.

To eliminate the p term, we can multiply equation 1 by -1 and add it to equation 2:

-1(p + n) = -1(115)
-1p - 1n = -115

p + 4.25n = 358.75
-1p - 1n = -115

Summing these two equations, we get:

3.25n = 243.75

Dividing both sides by 3.25, we find:

n = 75

Now we can substitute the value of n back into one of the original equations. Let's use equation 1:

p + n = 115
p + 75 = 115

Subtracting 75 from both sides, we find:

p = 40

Therefore, 40 pounds of peanuts and 75 pounds of pecans were sold.