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.

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

Answer 1

"(31.0, 71.0)There were 31.0 pounds of almonds and 71.0 pounds of macadamia nuts sold at the fair."

Explanation:

We need to use substitution to solve the system of equations shown. The equations are:

`p+n=102`

`p+5.93n=452.03`

Solving first one for p, we get:

p = 102 - n

Putting this in 2nd, we get:

(102 - n) + 5.93n = 452.03

4.93n = 350.03

n = 71

Now, we know p = 102 - n, so

p = 102 - 71 = 31

Hence,

Number of almonds is 31

Number of macadamia = 71

Fourth answer choice is right.