Question

A nut mixture of almonds and macadamia nuts at a small fair is $1.00 per pound of almonds and $3.52 per pound of macadamia nuts. Over the entire day, 125 pounds of the nut mixture were sold for $316.52. 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=125p+3.52n=316.52 Determine the correct description and amount of pounds for almonds and macadamia nuts that were sold.

Answer 1

the system of equations that models this scenario is:

p+n=125 ----> first equation

p+3.52n=316.52 -----> second equation

p is the number almonds and n is the number of macadamia nuts

Now we solve both equation and find out p and n

Solve the first equation for p

p+n=125 (subtract n from both sides)

p = 125 - n

Now plug it in second equation

`p + 3.52n = 316.52`

`125 - n + 3.52n = 316.52`

`125 + 2.52n = 316.52`

`2.52n = 316.52- 125`

`2.52n = 191.52` (divide by 2.52)

n = 76

We know p = 125 - n

p = 125 - 76 = 49

Number of pounds of almonds = 49 pounds

Number of pounds of macadamia nuts = 76 pounds

The cost of almond is $1 per pound

So the cost of 49 pounds of almond = $49

The cost of macadamia nuts is $3.52 per pound

So the cost of 76 pounds of almond = $267.52