Answer
1 hour of Horseback Riding costs: 30.00 dollars
1 hour of parasailing costs: 51.00 dollars.
Work Step by Step
First lets take a look at the two packages offered by the hotelL:
1. Cost= 192 dollars, 3 hours of horseback riding, 2 hours of parasailing
2. Cost= 213 dollars, 2 hours of horseback riding, 3 hours of parasailing
Then lets substitute:
- the cost as (c)
- the cost of 1 hour of horseback riding as (r)
- the cost of 1 hour of parasailing as (p)
Now we can create the two equations/systems to represent the problem. The coefficient of the variables "r" and "p" represent the number of hours of each activity.
1. 3r+2p=192
2. 2r+3p=213
Then lets multiply the first equation by a scalar of 2 and the second equation by a scalar of 3. Now our two equations look like:
1. 6r+4p=384
2. 6r+9p=639
Now lets subtract the second equation from the first equation now that we have the same coefficient of r and would allow us to eliminate all of the r-variables. We get the equation:
-5p=-255
Divide by -5 on both sides to isolate "p"
p=51.
Now that we have the cost of 1 hour of parasailing lets substitute into our first original equation to find the cost of horseback riding.
3r+2(51)=192
3r+102=192
Subtract 102 from both sides and also divide by 3 on both sides of the equation after. We get:
r=30.
So the cost of 1 hour of horseback riding is 30.00 dollars and the cost of 1 hour of parasailing is 51.00 dollars.
