Question

A hotel offers two activity packages. One costs $192 and includes 3 h

Answer 1

Answer:

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

Step-by-step 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  $p$ :

$3h+2p=192\\3h=192-2p\\h=\frac{192-2p}{3}$

$2(\frac{192-2p}{3})+3p=213\\\frac{384-4p}{3}+3p=213\\\frac{384-4p+9p}{3}=213\\384+5p=639\\5p=639-384\\5p=255\\p=51$

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