Greg's favorite snack is apples and cheese. Last week, he bought 2 pounds of apples and
$5.73 worth of cheese. This week, he bought pounds of apples and $6.54 worth of
cheese. Greg realized that he spent the exact same amount each week.
What is the price of one pound of apples?
To find the price of one pound of apples, we need to set up an equation based on the information given.
Let's assume that the price of one pound of apples is "x."
According to the given information, Greg spent $5.73 on cheese and "2 pounds" of apples last week, and $6.54 on cheese and "y pounds" of apples this week.
The equation can be set up as follows:
2x + 5.73 = yx + 6.54
Now, let's solve this equation to find the value of x, which represents the price of one pound of apples.
2x + 5.73 = yx + 6.54
Rearranging the equation, we get:
2x - yx = 6.54 - 5.73
(2 - y)x = 0.81
Dividing both sides by (2 - y), we get:
x = 0.81 / (2 - y)
Therefore, the price of one pound of apples is "0.81 / (2 - y)."
Let's assume that the price of one pound of apples is x dollars.
So, last week Greg spent 2x dollars on apples.
Also, last week Greg spent a total of $5.73 on cheese.
Therefore, he spent a total of 2x + $5.73 on his favorite snack last week.
Similarly, this week Greg spent a total of x + $6.54 on his favorite snack.
Since he spent the exact same amount each week, we can set up the equation 2x + $5.73 = x + $6.54.
Subtracting x from both sides of the equation, we get x + $5.73 = $6.54.
Now, subtracting $5.73 from both sides of the equation, we have x = $6.54 - $5.73.
Simplifying the right side of the equation, we get x = $0.81.
Therefore, the price of one pound of apples is $0.81. Answer: \boxed{0.81}.