SOLUTION: While waiting for your car to be fixed, you and your friends go to Dim Sum Restaurant for food (the popcorn and pretzels were not enough). All small dishes cost the same and all l

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Question 1208974: While waiting for your car to be fixed, you and your friends go to Dim Sum Restaurant for food
(the popcorn and pretzels were not enough). All small dishes cost the same and all large dishes
cost the same. Before tip, your bill of 3 small dishes and 5 large dishes was $28.20. A bill at
another table for 4 small dishes and 3 larges dishes was $23.30. How much is each a small and
large dish alone?
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
                    PRICE      QTY     COST   |     QTY    COST
                                              |
small dish           c          3       3c    |     4      4c
                                              |
large dish           g          5       5g    |     3      3g
  
COST                                   28.20             23.30

system%283c%2B5g=28.2%2C4c%2B3g=23.3%29
Solve the system.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

x = cost of 1 small dish
y = cost of 1 large dish
Each cost is in dollars.

3 small + 5 large = $28.20
3x+5y = 28.20

4 small + 3 large = $23.30
4x+3y = 23.30

We can form this system of equations
system%283x%2B5y+=+28.20%2C4x%2B3y+=+23.30%29

Let's say we want to eliminate the x variable.
If we add the equations straight down we get 3x+4x = 7x, but we want the x values to go to 0.

We can quadruple both sides of the original equation.
Also we can multiply both sides of the 2nd equation by -3 to get this equivalent system.
system%2812x%2B20y+=+112.80%2C-12x-9y+=+-69.90%29
At this point the x coefficients are equal in absolute value, but have opposite sign.

Add straight down.
The x terms add to 0.
The y terms add to 11y
The right hand sides add to 42.90

We arrive at 11y = 42.90
Divide both sides by 11 to get y = 42.90/11 = 3.90
This result is exact and hasn't been rounded.
One large dish costs $3.90

Since we know the value of y, we can use it to find x.
Use any of the equations mentioned.
3x+5y = 28.20
3x+5*3.90 = 28.20
3x+19.50 = 28.20
3x = 28.20-19.50
3x = 8.70
x = 8.70/3
x = 2.90
This result is exact and hasn't been rounded.

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Answers:
One small dish costs $2.90
One large dish costs $3.90
I'll leave the verification for the student to do.