The regular price of a child's entry ticket to a water park is $6 less than that for an adult'a. The park offers half off all entry tickets during the off-peak season. The Jordan's paid a total of $69 for two adult tickets and one child's ticket to the waterpark during the off-peak season. The following equation represents this situation, where x represents the regular price of an adult ticket : 69 = x + 1/2 (x - 6) What is the regular price of a child's ticket?

Question

The regular price of a child's entry ticket to a water park is $6 less than that for an adult'a. The park offers half off all entry tickets during the off-peak season. The Jordan's paid a total of  $69 for two adult tickets and one child's ticket to the waterpark during the off-peak season. The following equation represents this situation, where x represents the regular price of an adult ticket : 69 = x + 1/2 (x - 6)  What is the regular price of a child's ticket?

anonymous · Answer

They give you the equation, what are you having trouble with?

imstuck · Answer

I'm guessing the problem is in solving for x right?

anonymous · Answer

69 = x + 1/2(x - 6)
69 = x + x/2 - 3

anonymous · Answer

Is that right IM?

imstuck · Answer

Yes, that's good...keep going... ; )

anonymous · Answer

69 = x + x/2 - 3
72 = x + x/2
2(72 = x + x/2)
Correct?

imstuck · Answer

What do you get for x?

anonymous · Answer

144 = 2x + x
144 = 3x
48 = x

imstuck · Answer

If you solve it using your equation you will get it wrong.  You need to find the common denominator between the x and the x/2.

anonymous · Answer

Okay
so x / 1 + x / 2
2x / 2 + x / 2
2x + x

anonymous · Answer

...

anonymous · Answer

what is wrong with me?

imstuck · Answer

I get this:$$69=x+\frac{ 1 }{ 2 }x-3$$then$$72=\frac{ 2 }{ 2 }x+\frac{ 1 }{ 2 }x$$then$$72=\frac{ 3 }{ 2 }x$$

anonymous · Answer

That's because I said x/2 and not 1/2(x) because I derped the derp up.

imstuck · Answer

Multiply both sides by 2 to get rid of the fraction and it is now 144=3x and x = 48.  Right.  BUT...

imstuck · Answer

They want the price of a child's REGULAR admission ticket and x is the amount of an adult ticket at reduced price.  Now we need to find the price of a regular child's ticket.  Any ideas on that?

imstuck · Answer

They tell you in the problem that the special is half off the regular price when it is off-season.  If $48 is the price during off-season, how do you find the price during peak season?  What is your equation for that?

anonymous · Answer

You'd multiply it by 2.

imstuck · Answer

Yep.  So now you have the regular price of an adult ticket.  What do they tell you about the price of a child's ticket in regards to the adult's ticket?  How much less is the child's ticket?

anonymous · Answer

if x is equal to 48 and a regular child's ticket it 6$ less than an adults ticket wouldn't you just subtract 6 and get 42?

anonymous · Answer

The answer choices are 
$38 
$42 
$48 
and 
$66

mathstudent55 · Answer

$69 = x + 1/2 (x - 6)$

Multiply both sides by 2:

138 = 2x + x - 6

138 = 3x - 6

144 = 3x

x = 48

anonymous · Answer

48 was the wrong answer

mathstudent55 · Answer

48 is x.
I didn't say the answer is x.
x is the price for an adult. The price for a child is $48 - $6 = $42.

I was just showing how I solve the equation because I wanted to show the way I get rid of the denominator early on.