Samantha is going on a vacation for the summer and is trying to choose between two different plans. The first plan costs 450$ for 3 days at a hotel and 2 days at an amusement park. The second plan offers 5 days at the same hotel and 3 days at the amusement park for 700$. The cost of 1 day at the hotel and the amusement park is the same under both plans. How much does a 1 day trip to the amusement park cost? ((I think it's 50$)) ??
hotel costs $h/day
park costs $p/day
3h + 2p = 450
5h + 3p = 700
15h + 10p = 2250
15h + 9p = 2100
subtract:
p = 150
so, h=50
3(50)+2(150) = 150 + 300 = 450
5(50)+3(150) = 250 + 450 = 700
SO, it looks like you solved the problem, but got the hotel and park switched.
To find the cost of a 1-day trip to the amusement park, we'll need to compare the two plans and calculate the cost of each option.
Let's assume the cost of 1 day at the hotel is 'H' dollars and the cost of 1 day at the amusement park is 'A' dollars.
According to the given information, the first plan costs $450 for 3 days at the hotel and 2 days at the amusement park. This can be written as:
3H + 2A = $450
Similarly, the second plan costs $700 for 5 days at the hotel and 3 days at the amusement park. This can be written as:
5H + 3A = $700
Now, we can solve these two equations simultaneously to find the values of 'H' and 'A'.
Multiplying the first equation by 3 and the second equation by 2, we get:
9H + 6A = $1350
10H + 6A = $1400
By subtracting the equations, we find:
10H - 9H = $1400 - $1350
H = $50
Now, we can substitute the value of 'H' into either of the original equations to find 'A'.
Using the first equation:
3(50) + 2A = $450
150 + 2A = $450
2A = $300
A = $150
So, the cost of a 1-day trip to the amusement park is $150, not $50 as you thought.