Question

Elisa and Katy are both traveling to Europe. Elisa paid $820 for her plane ticket and $110.50 per night for her hotel. Katy paid $1,205 for her plane ticket and $75.50 per night for her hotel. They each spent the same number of nights in their hotels. The two women each spent the same total amount for airfare and lodging during their trips. Set up a system of equations to model the amount of money Elisa and Katy spend on airfare and lodging during their trips. Let x represent the number of nights spent in a hotel, let E represent the total amount Elisa spends, and let K represent the total amount Katy spends.

Answer 1

820 + 110.50x = E

1205 + 75.50x = K

Step-by-step explanation

Let x represent the number of nights spent in a hotel.

Let E represent the total amount Elisa spends.

Let K represent the total amount Katy spends.

We have that Elisa paid $820 for her plane ticket and $110.50 per night for her hotel.

This means that the total amount that Elisa spent after x nights is:

820 + 110.50 * x = E

=> 820 + 110.50x = E

We also have that Katy paid $1205 for her plane ticket and $75.50 per night for her hotel.

This means that the total amount that Katy spent after x nights is:

1205 + 75.50 * x = K

1205 + 75.50x = K

The system of equations that model the amount of money that Elisa and Katy spend during their trips is:

820 + 110.50x = E

1205 + 75.50x = K