SOLUTION: Forty students bought caps at the baseball game. Plain caps cost $4 each and deluxe ones cost $6 each. If the total bill was $236, how many students bought the deluxe cap?

Algebra ->  Expressions-with-variables -> SOLUTION: Forty students bought caps at the baseball game. Plain caps cost $4 each and deluxe ones cost $6 each. If the total bill was $236, how many students bought the deluxe cap?      Log On


   

Question 513355: Forty students bought caps at the baseball game. Plain caps cost $4 each and deluxe ones cost $6 each. If the total bill was $236, how many students bought the deluxe cap?
Found 2 solutions by solver91311, oberobic:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!






Solve the system.

John

My calculator said it, I believe it, that settles it
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Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
p = number of plain caps
4p = price of plain caps
d = number of deluxe caps
6d = price of deluxe caps
.
p + d = 40
so
p = 40-d
.
4p + 6d = 236
.
substitute p = 40-d
.
4*(40-d) + 6d = 236
.
160 -4d + 6d = 236
.
2d = 76
.
d = 38
.
p = 40-d
p = 40-38
p = 2
.
They appear to have bought 38 deluxe caps and 2 plain caps.
.
But always check your answer! (I got it wrong the first time myself, and I've been doing algebra for 45 years.)
You used the first equation to find p, so you need to use the other equation to check the solution.
(Don't fall into the trap of using the same equation twice.)
.
4p + 6d = 236
4(2) + 6(38) = ??
8 + 228 = 236
Correct.
.
Answer: 38 students bought deluxe caps.
.
Done.