SOLUTION: River Joes's Seafood Diner charges $6.00 for a catfish dinner and $3.50 for an order of popcorn shrimp. After filling 26 orders for popcorn shrimp and catfish dinners, River Joe h

Question 694412: River Joes's Seafood Diner charges $6.00 for a catfish dinner and $3.50 for an order of popcorn shrimp. After filling 26 orders for popcorn shrimp and catfish dinners, River Joe had collected $133.50. How many orders of popcorn shrimp and catfish dinners did they sell?
Found 2 solutions by checkley79, stanbon:
Answer by checkley79(3341) (Show Source): You can put this solution on YOUR website!
C+S=26 MULTIPLY BY -3.5 & ADD.
6C+3.5S=133.50
-3.5C-3.5S=-91
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2.5C=42.5
C=42.5/2.5
C=17 CATFISH DINNERS WERE SOLD.
17+S=26
S=26-17
S=9 SHRIMP DINNERS WERE SOLD.
PROOF:
6*17+3.5*9=133.50
102+31.50=133.50
133.5=133.50
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
River Joes's Seafood Diner charges $6.00 for a catfish dinner and $3.50 for an order of popcorn shrimp. After filling 26 orders for popcorn shrimp and catfish dinners, River Joe had collected $133.50. How many orders of popcorn shrimp and catfish dinners did they sell?
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Quantity Eq:::: p + c = 26 orders
Value Eq::: 3.5p +6c = 133.5 dollars
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Multiply thru top by 35
Multiply thru bottom by 10
--------------------------------
35p + 35C = 35*26
35p + 60c = 1335
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Subtract and solve for "c":
25c = 425
catfish = 17 (# of catfish orders)
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Solve for "p":
p + c = 26
p + 17 = 26
p = 9 (# of popcorn schrimp orders)
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Cheers,
Stan H.
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