A nut mixture of almonds and cashew nuts at a small fair is $1.00 per pound of almonds and $3.55 per pound of cashew nuts. Over the entire day, 65 pounds of the nut mixture were sold for $189.95. If p is the number almonds and n is the number of cashew nuts, then the system of equations that models this scenario is: p+n=65 p+3.55n=189.95 Determine the correct description and amount of pounds for almonds and cashew nuts that were sold

p = 16

n = 49

Step-by-step explanation:

p + n = 65

p + 3.55n = 189.95

To solve this system of equations, you have to use substitution.  This means that you have to set one equation equal to one of the variables.  You then have to substitute that variable into the second equation.

Rearrange the first equation so that it equals p.

p + n = 65

p = 65 - n

Substitute the p-value into the second equation.

p + 3.55n = 189.95

(65 - n) + 3.55n = 189.95

Solve for n.

65 - n + 3.55n = 189.95

65 + 2.55n = 189.95

(65 + 2.55n) - 65 = 189.95 - 65

2.55n = 124.95

(2.55n)/2.55 = 124.95/2.55

n = 49

Use this n-value to solve for p.  You can pick whichever equation you want to solve for p and get the same answer.  I will use the first answer.

p + n = 65

p + 49 = 65

(p + 49) - 49 = 65 - 49

p = 16

There are 16 pounds of almonds and 49 pounds of cashews.