Question

A nut mixture of almonds and cashew nuts at a small fair is $1.00 per pound of almonds and $3.09 per pound of cashew nuts. Over the entire day, 89 pounds of the nut mixture were sold for $201.86. 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=89p+3.09n=201.86p+n=89p+3.09n=201.86

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

Answer 1

The answer to the question

Answer 2

Answer: (35.0, 54.0)

There were 35 pounds of almonds and 54 pounds of cashew nuts sold at the fair.

Explanation:

Given : 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=89-----------(1)\\\\p+3.09n=201.86----------(2)`

To solve the above system , we subtract equation (1) from (2), we get

`3.09n-n=201.86-89\\\\\Rightarrow\ 2.09=112.86\\\\\Rightarrow\ n=54`

Now, put the value of 'n' in (1) , we get

`p+54=89\\\\\Rightarrow\ p=89-54=35`

Hence, There were 35 pounds of almonds and 54 pounds of cashew nuts sold at the fair.