Two cups, two plates, and a pot cost $10.20 at a garage sale. A cup costs twice as much as a plate. The pot costs $3 more than a cup. What is the price of the pot? Explain how you got your answer.

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To find the price of the pot, we can start by assigning variables to the unknown quantities. Let's say the price of a cup is "x" dollars, the price of a plate is "y" dollars, and the price of the pot is "z" dollars.

From the given information, we know that a cup costs twice as much as a plate. Therefore, we can write the equation:
x = 2y (Equation 1)

We also know that the pot costs $3 more than a cup, which can be expressed as:
z = x + 3 (Equation 2)

Now, we need to use the information about the total cost of the cups, plates, and pot to form another equation. We are told that two cups, two plates, and a pot cost $10.20. Since there are two cups, the total cost of the cups is 2x. Similarly, the total cost of the plates is 2y. Therefore, the equation becomes:
2x + 2y + z = 10.20 (Equation 3)

We now have three equations:
1) x = 2y
2) z = x + 3
3) 2x + 2y + z = 10.20

To solve this system of equations, we can substitute the value of "x" from Equation 1 into Equation 3.
Substituting x = 2y in Equation 3, we get:
2(2y) + 2y + z = 10.20
4y + 2y + z = 10.20
6y + z = 10.20 (Equation 4)

We also need to substitute the value of "x" from Equation 1 into Equation 2.
Substituting x = 2y in Equation 2, we get:
z = (2y) + 3
z = 2y + 3 (Equation 5)

Now we have two equations:
4y + z = 10.20 (Equation 4)
z = 2y + 3 (Equation 5)

To isolate "z" in Equation 5, we can subtract 2y from both sides:
z - 2y = 3

Now we can substitute this value of z in Equation 4:
4y + (z - 2y) = 10.20
4y + z - 2y = 10.20
2y + z = 10.20

This equation is equivalent to Equation 4, so we can conclude that Equation 4 and Equation 5 represent the same relationship. Hence, we can solve either equation to find the price of the pot.

Let's solve Equation 4:
2y + z = 10.20

Since Equation 1 gives us the relationship x = 2y, we can substitute 2y for x in Equation 2, and it becomes:
2y + z = 10.20

Now we have two variables (y and z) in Equation 4. However, we only have one equation, so we cannot solve for both y and z unless we have additional information.

Therefore, the answer cannot be determined with the given information.