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=452.03p+n=102p+5.93n=452.03 Determine the correct description and amount of pounds for almonds and macadamia nuts that were sold

Answer 1

Total pounds sold:
we know that p pounds of almonds and n pounds of nuts were sold.
The total pounds were 102 pounds.
Therefore:
n + p = 102 ............> equation I
Therefore:
p = 102-n ..............> equation II

For almonds:
1 pound of almonds costs $1, therefore:
p pounds of almonds would cost 1*p = $p

For macadamia:
1 pound of macadamia costs $5.93, therefore:
n pounds of macadamia would cost 5.93*n = $5.93n

The total amount paid for both types was $452.03, therefore:
$p + $5.93n = $452.03 ............> equation III

Substitute with equation II in equation III:
102-n+5.93n = 452.03
4.93n = 350.03
n = 71 pounds
Substitute with the value of n in equation 1 to get p as follows:
n+p = 102
p = 102-n = 102-71 = 31 pounds

Total cost of almonds = $p = $31
Total cost of macadamia = $5.93n = 5.93(71) = $421.03

Therefore, based on the above calculations:
number of pounds of almonds = 31 pounds
cost of almonds = $31
number of pounds of macadamia = 71 pounds
cost of macadamia = $421.03