Question

A nut mixture of peanuts and pecans at a small fair is $1.00 per pound of peanuts and $2.85 per pound of pecans. Over the entire day, 97 pounds of the nut mixture were sold for $254.25. If p is the number peanuts and n is the number of pecans, then the system of equations that models this scenario is:

p+n=97
p+2.85n=254.25

Determine the correct description and amount of pounds for peanuts and pecans that were sold.
A (12.0, 85.0)There were 12.0 pounds of peanuts and 85.0 pounds of pecans sold at the fair.
B (75.0, 22.0)There were 75.0 pounds of peanuts and 22.0 pounds of pecans sold at the fair.
C (85.0, 12.0)There were 85.0 pounds of peanuts and 12.0 pounds of pecans sold at the fair.
D (22.0, 75.0)There were 22.0 pounds of peanuts and 75.0 pounds of pecans sold at the fair.

I NEED HELP ASAP

Answer 1

A - 12.0, 85.0
You can solve this system of equations by subtracting p+2.85n-p-n=254.25-97 and if you solve that, you get 1.85n=57.25 and that can be simplified to n=85

Answer 2

A. (12.0, 85.0)There were 12.0 pounds of peanuts and 85.0 pounds of pecans sold at the fair.

Explanation:

Here, the given system of equations,

p + n = 97 ------(1)

p + 2.85n = 254.25 -----(2)

Where,

p = number of pounds of peanuts,

n = number of pounds of pecans,

Equation (2) - equation (1),

We get,

1.85n = 157.25,

`\implies n = (157.25)/(1.85)=85`

From equation (1),

p + 85 = 97 ⇒ p = 97 - 85 = 12,

Thus, there were 12.0 pounds of peanuts and 85.0 pounds of pecans sold at the fair.

i.e. the solution of the above system of equation is (12.0, 85.0)

OPTION A is correct.