SOLUTION: A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and h

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and h      Log On


   

Question 335935: A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A caterer is planning a party for 64 people. The customer has $150 to spend. A $39 pan of pasta feeds 14 people and a $12 sandwich tray feeds 6 people. How many pans of pasta and how many sandwich trays should the caterer make?
----------------------------
People Equation: 14p + 6t = 64 people
Value Equation: 39p + 12t = 150 dollars
---------------------------------------------
Multiply thru the 1st equation by 12.
Multiply thru the 2nd equation by 6.
-----------------------------------------
12*14p + 12*6t = 12*64
6*39p + 6*12t = 6*150
------------------------------
Subtract 1st from 2nd and solve for "p":
66p = 132
p = 2 (# of pans of pasta needed)
-----
Substitute into 14p+6t = 64 and solve for "t":
28 + 6t = 64
6t = 36
t = 6 (# of sandwich trays needed)
===================================
Cheers,
Stan H.