SOLUTION: A department store held a sale to sell all of the 214 winter jackets that remained after the season ended. Unitl noon, each jacket in the store was priced at $31.95. At noon, the p

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: A department store held a sale to sell all of the 214 winter jackets that remained after the season ended. Unitl noon, each jacket in the store was priced at $31.95. At noon, the p      Log On


   

Question 708691: A department store held a sale to sell all of the 214 winter jackets that remained after the season ended. Unitl noon, each jacket in the store was priced at $31.95. At noon, the price of the jackets was further reduced to $18.95. After the last jacket was sold, total receipts for the clearance sale were $5108.30. How many jackets were sold before noon and how many were sold after noon?
Make a system to solve.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of jackets were sold before noon (at $31.95 each)
y = number of jackets were sold after noon (at $18.95 each)
All 214 jackets were sold, so
highlight%28x%2By=214%29
Before noon, the money received for selling x jackets at $31.95 each was
$31.95x
After noon, the amount received for selling y jackets at $18.95 each was
$18.95y
The total receipts of the clearance sale (all the money received for selling those jackets, in $ was
highlight%2831.95x%2B18.95y=5108.30%29
Those two equations form the system
system%28x%2By=214%2C31.95x%2B18.95y=5108.30%29
The first equation times 18.95,
18.95x%2B18.95y=18.95%2A214 --> 18.95x%2B18.95y=4055.30
can be subtracted from the second one to get
31.95x-18.95x=5108.30-4055.30 --> 13x=1053 --> x=1053%2F13 --> highlight%28x=81%29
That along with x%2By=214 result in
81%2By=214 --> y=214-81 --> highlight%28y=133%29