SOLUTION: Lorena bought 10 packs of styrofoam cups for the graduation dance. a pack of fifty 12-oz cups costs $1.80 and apack of fifty 16-oz cups costs $2.40. Lorena paid a total of $21.60 e

Algebra ->  Systems-of-equations -> SOLUTION: Lorena bought 10 packs of styrofoam cups for the graduation dance. a pack of fifty 12-oz cups costs $1.80 and apack of fifty 16-oz cups costs $2.40. Lorena paid a total of $21.60 e      Log On


   



Question 181451: Lorena bought 10 packs of styrofoam cups for the graduation dance. a pack of fifty 12-oz cups costs $1.80 and apack of fifty 16-oz cups costs $2.40. Lorena paid a total of $21.60 excluding tax. How many packs of each size cup did she buy?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = the number of packs of 12 oz cups she bought
Let b = the number of packs of 16 oz cups she bought
given:
(1) a+%2B+b+=+10
(2) 180a+%2B+240b+=+2160
Multiply both sides of (1) by 180 and subtract from (2)
(2) 180a+%2B+240b+=+2160
(1) -180a+-+180b+=+-1800
60b+=+360
b+=+6
and, since
(1) a+%2B+b+=+10
a+%2B+6+=+10
a+=+4
She bought 4 packs of 12 oz cups and
6 packs of 16 oz cups
check answer:
(2) 180a+%2B+240b+=+2160
(2) 180%2A4+%2B+240%2A6+=+2160
720+%2B+1440+=+2160
2160+=+2160
OK