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PROBLEM
CATERING: A CATERER IS PLANNING A PARTY FOR 64 PEOPLE. THE CUSTOMER HAS 150 DOLLARS 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.

SOLUTION:
EQUATION 1
PEOPLE PER PAN OF PASTA= 14
PANS OF PASTA=P
PEOPLE PER SANDWICH TRAY=6
SANDWICH TRAYS=S
PEOPLE AT PARTY=64

EQUATION 2
PRICE PER PAN OF PASTA=39
PANS OF PASTA=P
PRICE PER SANDWICH TRAY=12
SANDWICH TRAYS=S
MONEY TO SPEND=150

ALGEBRAICALLY EXPRESSED EQUATIONS
14P+6S=64
39P+12S=150

I WILL USE LINEAR COMBINATION TO SOLVE IT
MULTIPLY EQUATION 1 BY -2
-28P-12S=-128
39P+12S=150

ADD THESE TWO EQUATIONS TO GET
P=2

SUBSTITUTE BACK IN TO ONE OF THE ORIGINAL EQUATIONS AND SOLVE FOR S
14(2)+6S=64
SOLVE TO GET
S=6

SO THE SOLUTION IS THE CATERER SHOULD MAKE TWO PANS OF PASTA AND 6 SANDWICH TRAYS FOR THE PARTY.