Question

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?

Answer 1

Cost of 1 hour of horseback riding is $30 and cost of 1 hour of parasailing is $51.

Explanation:

Let cost of horseback riding be
`h`

Let cost of parasailing be
`p`

• "First Package costs $192 and includes 3 h of horseback riding and 2 h of parasailing. "

We can write
`3h+2p=192`

• "Second Package costs $192 and includes 3 h of horseback riding and 2 h of parasailing. "

We can write
`2h+3p=213`

Solving these 2 equations simultaneously will give us cost of horseback riding for 1 hours [h] and cost of parasailing for 1 hours [p].

Solving for
`h` in Equation 1 and substituting that in Equation 2, we can solve for
`p` :

`3h+2p=192\\3h=192-2p\\h=(192-2p)/(3)`

`2((192-2p)/(3))+3p=213\\(384-4p)/(3)+3p=213\\(384-4p+9p)/(3)=213\\384+5p=639\\5p=639-384\\5p=255\\p=51`

Now, taking the value
`p=51` and putting it in either equation and solving for
`h` will give us the value of
`h` . Let's substitute it into Equation 1:

`3h+2(51)=192\\3h+102=192\\3h=192-102\\3h=90\\h=30`

Hence, cost of 1 hour of horseback riding is $30 and cost of 1 hour of parasailing is $51.

Answer 2

we are given with two hotel offers: $192 for 3h horseback riding and 2h parasailing and the other one: $213 for 2 h horseback riding and 3h parasailing. IN this case, we translate the statements into equations:
192 = 3x + 2y213 = 2x + 3y
x = 30y = 51
Hence, the cost for one hour each is $30 for horseriding and $51 for parasailing