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
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 <span>macadamia: </span>1 pound of <span>macadamia costs $5.93, therefore: n pounds of </span><span>macadamia would cost 5.93*n = $5.93n
The total amount paid for both types was </span><span>$452.03, therefore: $p + $5.93n = </span><span>$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 = </span>$421.03
Using linear functions would not be appropriate to find the number of black bears in 2015 because it increases and decreases randomly. We cannot figure out the exact amount with linear functions.