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
