Let's define the variable $x$ as the cost of one bag of apples.

Given:

• The total cost is $47.45.
• The total cost for the eggs is $6.77.
• Katherine buys 6 bags of apples.

The total cost for the apples is $6x$ since there are 6 bags, and each costs $x$.

The equation representing the total cost is:

$6x + 6.77 = 47.45$

To solve for $x$:

1. Subtract 6.77 from both sides:

$6x = 47.45 - 6.77$

$6x = 40.68$

2. Divide both sides by 6 to find $x$:

$x = \frac{40.68}{6}$

$x = 6.78$

So, each bag of apples costs $6.78.

Would you like more details or have any questions? Here are some related questions to consider:

1. What is the cost of 3 bags of apples?
2. If Katherine bought 10 bags of apples instead of 6, what would the total cost be?
3. How much change would Katherine get if she paid with $50?
4. How much would she pay if the price of each bag increased by $1?
5. What if the total cost was $55 instead of $47.45; how much would each bag cost then?

Tip: Always verify the solution by plugging the value back into the original equation to check if it satisfies the equation.