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.(75.0, 22.0) There were 75.0 pounds of peanuts and 22.0 pounds of pecans sold at the fair.
B.(12.0, 85.0) There were 12.0 pounds of peanuts and 85.0 pounds of pecans sold at the fair.
C.(22.0, 75.0) There were 22.0 pounds of peanuts and 75.0 pounds of pecans sold at the fair.
D.(85.0, 12.0) There were 85.0 pounds of peanuts and 12.0 pounds of pecans sold at the fair.

Answer 1

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

Explanation:

Subtract the first equation from the second:

1.85n = 157.25

n = 157.25/1.85 = 85 . . . . . divide by the coefficient of n

Only one answer choice has 85 pounds of pecans—the one shown above.