A hotel offers two activity packages. One costs $192 and includes 3 hrs of horseback riding and 2 hrs of para-sailing. The second costs $213 and includes 2 hrs of horseback riding and 3 hrs of para-sailing. What is the cost for 1 hr of each activity?

Question

stormoshawty · Answer

@OwlCoffee

owlcoffee · Answer

okay, so this is clearly a problem where we have to use a system of equations.
so let's say the hours of horseback riding is "m" and the para sailing hours is "n".
The first package says that it costs $192 and includes 3 hours of "m" and 2 hours of "n".
The second one costs $213 but includes 2 hours of "m" and 3 hours of "n".
Let's tradcue them into two equations:
$$3m+2n=192$$
$$2m+3n=213$$
Sine we've been using elimination to do the other two, let's use that for this one.
I'll multiply the first equation by -3 and the second by 2:
$$-9m-6n=-576$$
$$4m+6n=426$$
Now, let's sum the equations, reorder and operate the variables with constants:
$$-5m=-150$$
So, solving for "m" we get that m=30.
Let's replace it on the initial equations:
$$3(30)+2n=192$$
Sustracting 90 on each sides and operating:
$$2n=102$$
so we get that n=51
we can conclude that:
$$m=30$$
$$n=51$$
Traducing it to the problem, the cost of horseback riding hours are $30 each and the cost of para-sailing hours are $51 each.