Question

Emma is going on vacation this summer and is trying to choose between two different travel plans. The first plan costs $450 for 3 days at a hotel and 2 days at King's Island. The second plan offers 5 days at the same hotel and 3 days at King's Island for $700. The cost of at the hotel and King's Island is the same under both plans. How much does a 1-day trip to King's Island cost?

Answer 1

@fallonbanks

Answer 2

@One098

Answer 3

Do you have any idea as to what the answer might be?

Answer 4

I know how to find the answer, I just don't know how to set up the equations.

Answer 5

Alright, give me a sec.

Answer 6

Well you can make the first one something like:
450=3h+2k
h=cost per night at the hotel
k=cost per night at King's Island

Answer 7

or it should be more like the cost per day because that's what it implies.. "cost per day."

Answer 8

So the second one would be 700= 5h + 3k?

Answer 9

Exactly what I was about to say! So, yes!

Answer 10

Alright, I got it, thanks!

Answer 11

My pleasure, anytime!

Answer 12

I don't got it, what's next?

Answer 13

Lol. Alright, well you first want to solve for h, okay? So isolate the h.

Answer 14

Wait, no. Move the h to the left side of the equal sign.

Answer 15

Still lost?

Answer 16

Hm alright then.
\[450=3h+2k\]
Divide both sides by 3h:
\[\frac{ 450 }{ 3h }=\frac{ 3h }{ 3h }+2k\]
The 3h/3h cancel out.

Answer 17

Brilliant!

Answer 18

Do you know the next step?

Answer 19

No, sorry.

Answer 20

brb

Answer 21

Now you have:
\[\frac{ 450 }{ 3h }=2k\]

Answer 22

That's the equation i use to find the answer??

Answer 23

Yes and you must do the same to find the next equation, however I think there is another way, its simpler, to find the answers..

Answer 24

Which is what?

Answer 25

\[450=3h+2k\]
Instead, subtract 2k from both sides.

Answer 26

2k-450=3h?

Answer 27

Well you see, the 450 isn't a negative, so it must be positive. \[450-2k=3h\]