SOLUTION: a pizza shop delivered 16 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $128. a small pizza costs $4 and contains 3 ounces of pe

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: a pizza shop delivered 16 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $128. a small pizza costs $4 and contains 3 ounces of pe      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


   



Question 903962: a pizza shop delivered 16 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $128. a small pizza costs $4 and contains 3 ounces of pepperoni. a medium pizza costs $9 and contains 5 ounces of pepperoni. a large pizza cost $11 and contains 10 ounces of pepperoni. the owner of the pizza shop used 6 pounds 7 ounces of pepperoni in making the pizzas. how many pizzas of each size were delivered to the college?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = number of small pizzas delivered
Let +b+ = number of medium pizzas delivered
Let +c+ = number of large pizzas delivered
-----------------------------------------
(1) +a+%2B+b+%2B+c+=+16+
(2) +4a+%2B+9b+%2B+11c+=+128+
(3) +3a+%2B+5b+%2B+10c+=+6%2A16+%2B+7+
--------------------------------
(3) +3a+%2B+5b+%2B+10c+=+103+
Multiply both sides of (1) by +3+
and subtract (1) from (3)
(3) +3a+%2B+5b+%2B+10c+=+103+
(1) +-3a+-+3b+-+3c+=+-48+
---------------------------
+2b+%2B+7c+=+55+
--------------------
Multiply both sides of (1) by +4+
and subtract (1) from (2)
(2) +4a+%2B+9b+%2B+11c+=+128+
(1) +-4a+-+4b+-+4c+=+-64+
--------------------------
+5b+%2B+7c+=+64+
-----------------------
Subtract:
+5b+%2B+7c+=+64+
+-2b+-+7c+=+-55+
-------------------
+3b+=+9+
+b+=+3+
-------------
and,
+5%2A3+%2B+7c+=+64+
+7c+=+64+-+15+
+7c+=+49+
+c+=+7+
------------
(1) +a+%2B+b+%2B+c+=+16+
(1) +a+%2B+3+%2B+7+=+16+
(1) +a+=+6+
---------------
6 small
3 medium
7 large
were delivered