Question

A nut mixture of almonds and macadamia nuts at a small fair is $1.00 per pound of almonds and $5.93 per pound of macadamia nuts. Over the entire day, 102 pounds of the nut mixture were sold for $452.03. If p is the number almonds and n is the number of macadamia nuts, then the system of equations that models this scenario is:

p+n=102p+5.93n=452.03

Determine the correct description and amount of pounds for almonds and macadamia nuts that were sold.

A (61.0, 41.0)
There were 4.0 pounds of almonds and 36.0 pounds of macadamia nuts sold at the fair.
B (31.0, 71.0)
There were 31.0 pounds of almonds and 71.0 pounds of macadamia nuts sold at the fair.
C (41.0, 61.0)
There were 36.0 pounds of almonds and 4.0 pounds of macadamia nuts sold at the fair.
D (71.0, 31.0)
There were 71.0 pounds of almonds and 31.0 pounds of macadamia nuts sold at the fair.

Answer 1

p+n=102
p+5.93n=452.03

is your system

you can subtract the two equations (2nd eqn minus 1st eqn) to get

p - p = 0
5.93n - n = 4.93n
452.03 - 102 = 350.03

meaning 4.93n = 350.03

solve for n (the pounds of macadamia nuts) and choose the right solution based on this

gtg