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.
If the costs are x,y,z, respectively, then we have
2x+2y+z = 10.20
x = 2y
z = x+3
You want to find z.
To find the price of the pot, let's first assign some variables:
Let's say the price of a cup is "c" dollars, and the price of a plate is "p" dollars.
According to the information given, a cup costs twice as much as a plate, so we can write an equation:
c = 2p.
The pot costs $3 more than a cup, so we can write another equation:
pot = c + $3.
We also know that two cups, two plates, and a pot cost $10.20 in total. So we can write the equation:
2c + 2p + pot = $10.20.
Now, let's substitute the value of c from the first equation into the other two equations:
pot = (2p) + $3, and
2(2p) + 2p + (2p + $3) = $10.20.
Simplifying the second equation:
4p + 2p + 2p + $3 = $10.20,
8p + $3 = $10.20,
8p = $10.20 - $3,
8p = $7.20.
Now, divide both sides of the equation by 8 to isolate p:
p = $7.20 / 8,
p = $0.90.
So the price of a plate is $0.90.
Next, let's find the price of a cup by substituting the value of p into the first equation:
c = 2(0.90),
c = $1.80.
Therefore, the price of the cup is $1.80.
Finally, we can find the price of the pot by substituting the value of c into the equation for the pot:
pot = $1.80 + $3,
pot = $4.80.
Hence, the price of the pot is $4.80.
Cup $2
Plate $1
Pot $5