A hotel offers two activity packages. One costs $192 and includes 3 h of horseback riding and 2 h of parasailing. The second costs $213 and includes 2 h of horseback riding and 3 h of parasailing. What is the cost for 1 h of each activity?
A: Parasailing: $39; Horseback riding: $48
B: Parasailing: $51; Horseback riding: $30
C: Parasailing: $27; Horseback riding: $46
D: Parasailing: $63; Horseback riding: $24
Let's assume the cost for 1 hour of horseback riding is x and the cost for 1 hour of parasailing is y.
From the given information, we can create two equations:
3x + 2y = 192
2x + 3y = 213
Multiplying the first equation by 2 and the second equation by 3 to eliminate the x variable:
6x + 4y = 384
6x + 9y = 639
Subtracting the first equation from the second equation:
(6x + 9y) - (6x + 4y) = 639 - 384
5y = 255
y = 51
Plugging the value of y into the first equation:
3x + 2(51) = 192
3x + 102 = 192
3x = 90
x = 30
Therefore, the cost for 1 hour of horseback riding is $30 and the cost for 1 hour of parasailing is $51.
So, the answer is B: Parasailing: $51; Horseback riding: $30.