Word Problem
Catering 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?
Step 1: Write your equations. P is for pans and s is for trays. 64 is the number of people attending the party and 150 is the amount of money to spend on food.
14P + 6S = 64 |
Equation 1 Equation 2 |
Step 2: Use the linear combination method to solve the system. Multiply Equation 1 by -2 so that the coefficients of S differ only in sign. |
Step 3: Add the resolved equations and solve for P. |
Step 4: Substitute the value of P into one of the original equations and solve for S. |
-28P - 12S = -128 |
11P = 22 |
14P + 6S = 64 |
The caterer should make 2 pans of pasta and 6 sandwich trays for the party.