The regular price of a child's entry ticket to a water park is $6 less than that for an adult's. The park offers half off of all entry tickets during the off-peak season. The Jordans paid a total of $69 for 2 adult tickets and 1 child's ticket to the water park during the off-peak season. The following equation represents this situation, where x represents the regular price of an adult ticket.

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

jenniferjuice · Answer

someone help my brain hurts im sleepy ! please?!?

whpalmer4 · Answer

$$69 = x + \frac{x-6}{2}$$Why not start by multiplying everything by 2 to get rid of the fraction?

espex · Answer

So child = Adult - 6, off peak pricing = 1/2(peak pricing),
total off peak pricing = (2*adult) + (1*child) => (2*adult)+(1(adult-6))
If 'x' is the 'adult' and 69 is the total peak pricing, then your equation looks like $69 = 2x+1(x-6)$ multiply your answer by 2 to get the peak price of an adult, less 6 for a peak price of child.

whpalmer4 · Answer

Once you've solved that for $x$ remember that $x$ is the price of an adult ticket, and you want the price of a child's ticket, which is $6 less than an adult ticket.  Don't get tripped at the finish line :-)

espex · Answer

His equation was incorrect, it did not take into account the discount for all tickets.

espex · Answer

or, her equation. :)

whpalmer4 · Answer

yes, actually it does.  

69 = 2* adult + 1 * kid
these prices are off-peak, so they cost 50% less, and they've just collapsed 2*50% into x and kid/2

espex · Answer

Except that 69 is the discounted total.

whpalmer4 · Answer

Sigh.  Let Af be the price of a full-price adult ticket.  Cf is the price of a full-price child ticket, and = Af - 6.  Ad is the price of a discount adult ticket, and = Af/2.  Cd is the price of a discount child ticket, and = Cf/2 = (Af-6)/2.

They bought 2 adult discount tickets and 1 child discount ticket and paid $69.

$69 = 2*Ad + Cd = 2*(Af/2) + (Cf/2) = Af + (Af-6)/2

Now replace Af with x and you have...the equation from the problem statement.

espex · Answer

I stand corrected.

whpalmer4 · Answer

I scratched my head a few times looking at it when I first read it, too!