A golf resort offers the following two special packages. The Par 3 Package includes four nights of lodging and three rounds of golf for $443.50. The Par 5 Package includes seven night of lodging and five rounds of golf for $765.50. The rate for each night of lodging and for each round of golf are the same in both packages. How many dollars does one night's lodging cost?
cost of lodging ---x
cost of golf ------ y
4x + 3y = 443.50
7x + 5y = 765.5
1st times 5 --> 20x + 15y = 2217.5
2nd times 3 --> 21x + 15y = 2296.5
subtract them
x = 79
back in #1
etc
Thank you so very much.
To find the cost of one night's lodging, we need to determine the difference in the cost of the two packages and then divide it by the difference in the number of nights.
Let's start by comparing the Par 3 Package and the Par 5 Package:
The Par 3 Package includes four nights of lodging and three rounds of golf for a total cost of $443.50.
The Par 5 Package includes seven nights of lodging and five rounds of golf for a total cost of $765.50.
The difference in the cost of the packages is $765.50 - $443.50 = $322.
Now, let's find the difference in the number of nights:
The Par 5 Package includes seven nights of lodging, while the Par 3 Package includes four nights of lodging.
The difference in the number of nights is 7 - 4 = 3 nights.
To find the cost of one night's lodging, we divide the difference in cost ($322) by the difference in the number of nights (3):
$322 / 3 = $107.33
Therefore, one night's lodging costs $107.33.