Question

Can someone help me double check the equation to set up for this written problem?

Samantha is going on 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?

Answer 1

Where are your equations that you need to be checked?

Answer 2

Do you know where to start?

Answer 3

What is the equation you think is correct?

Answer 4

@Parrisc1 you there?

Answer 5

You need to set up a system of equations.
If you need help setting it up, let me know.
I'll show you how to do it step by step.

Answer 6

I need help setting it up I definitely did it wrong

Answer 7

@mathstudent55

Answer 8

Okay.

So first we have to set up a systems of equations. Now lets first get the variables.

How about we let \(\bf x\) mean the cost of 1 day at the hotel in the problem and \(\bf y\) can be the cost of 1 day at the amusement park in the problem.

Answer 9

So, we will just plug in the numbers used in the problem.

Now lets just make the systems of equations:

\(\bf \large 5x + 3y = 700\) \(\large \text {and}\) \(\bf \large 3x + 2y = 450\)

Answer 10

okay

Answer 11

Now solve the systems of equations.

Answer 12

So, lets solve it.

In the first equation lets subtract \(3y\) from both sides.

When you do that the equation should look like: \(5x = 700 - 3x\)

Answer 13

Now we divide 5 on both sides. Then plug in what you get for \(x\) in the second equation.

Then solve the second equation and you should find \(y\), which would be \(\bf \large y = \frac{94275}{629}\)

Answer 14

That's it! We didn't completely solve the systems of equations, but all we needed was y and we found it!

So now, to write it down easier we would divide 94275/629, which is.... what? Can you tell me?

@parrisc1

Answer 15

@AihberKhan
You did too many steps at once, and your answer is incorrect.
Your equations are correct. Your value for y is not.

Answer 16

1 day at hotel = x
1 day at park = y

3x + 2y = 450
5x + 3y = 700 -----> solve for x ---> 5x = 700 - 3y
x = 140 - (3/5)y

Substitute x into first equation:

3x + 2y = 450
3( 140 - (3/5)y ) + 2y = 450
420 - (9/5)y + 2y = 450
-(9/5)y + (10/5)y = 30
(1/5)y = 30
y = 150

The park costs $150 per day.

Answer 17

@mathstudent55

Sorry for doing too many steps at once but I did get $150 as well for the answer.