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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?

Verified Answer :

meerkat18

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

TaeKwonDoIsDead

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 @@MATH_TOKEN_2@@

  • "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.


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