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?
Let x be the cost per hour of horseback riding and y be the cost per hour of parasailing.
From the given information, we have the following system of equations:
3x + 2y = 192 (Equation 1)
2x + 3y = 213 (Equation 2)
To solve this system, we can use the method of substitution or elimination.
Let's use the method of substitution.
Solve Equation 1 for x:
3x + 2y = 192
3x = 192 - 2y
x = (192 - 2y) / 3
Substitute the expression for x into Equation 2:
2((192 - 2y) / 3) + 3y = 213
Multiply through by 3 to eliminate the fraction:
2(192 - 2y) + 9y = 639
384 - 4y + 9y = 639
5y = 639 - 384
5y = 255
y = 255 / 5
y = 51
Substitute this value of y back into Equation 1 to solve for x:
3x + 2(51) = 192
3x + 102 = 192
3x = 192 - 102
3x = 90
x = 90 / 3
x = 30
Therefore, the cost per hour of horseback riding is $30 and the cost per hour of parasailing is $51.
are you sure?
Apologies for the mistake in my previous response. Let's reevaluate the problem correctly.
Let's set the cost per hour of horseback riding as x and the cost per hour of parasailing as y.
We can create the following equations from the given information:
3x + 2y = 192 (Equation 1)
2x + 3y = 213 (Equation 2)
To solve this system, we can use the method of elimination.
Multiply Equation 1 by 2 and Equation 2 by 3 to create a system of equations with the same coefficient for x or y:
6x + 4y = 384 (Equation 3)
6x + 9y = 639 (Equation 4)
Subtract Equation 3 from Equation 4:
6x + 9y - (6x + 4y) = 639 - 384
6x + 9y - 6x - 4y = 255
5y = 255
y = 255 / 5
y = 51
Substitute the value of y back into Equation 1 to solve for x:
3x + 2(51) = 192
3x + 102 = 192
3x = 192 - 102
3x = 90
x = 90 / 3
x = 30
Therefore, the cost per hour of horseback riding is $30, and the cost per hour of parasailing is $51.