Greg's favorite snack is apples and cheese. Last week, he bought 2

Question

1
4
pounds of apples and $5.73 worth of cheese. This week, he bought 1
4
5
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?
$

Answer 1

Let \( x \) be the price of one pound of apples. The total cost for apples and cheese for each week can be expressed as follows:

For last week:

• Apples: \( 2.25x \) (since \( 2 \frac{1}{4} = 2.25 \))
• Cheese: \( 5.73 \)

Therefore, the total cost for last week can be written as: \[ 2.25x + 5.73 \]

For this week:

• Apples: \( 1.45x \) (since \( 1 \frac{4}{5} = 1.45 \))
• Cheese: \( 6.54 \)

Thus, the total cost for this week can be written as: \[ 1.45x + 6.54 \]

Since Greg spent the same amount each week, we can set the two equations equal to each other: \[ 2.25x + 5.73 = 1.45x + 6.54 \]

Now, let's solve for \( x \).

First, we can subtract \( 1.45x \) from both sides: \[ 2.25x - 1.45x + 5.73 = 6.54 \] This simplifies to: \[ 0.80x + 5.73 = 6.54 \]

Next, subtract \( 5.73 \) from both sides: \[ 0.80x = 6.54 - 5.73 \] Calculating the right side gives: \[ 0.80x = 0.81 \]

Now, divide both sides by \( 0.80 \) to solve for \( x \): \[ x = \frac{0.81}{0.80} = 1.0125 \]

Therefore, the price of one pound of apples is: \[ \boxed{1.01} \] (rounded to two decimal places).