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 Sandlers paid a total of $78 for 1 adult ticket and 2 child's tickets 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.

78 = one-halfx + (x - 6)

What is the regular price of a child's ticket?

help?

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 Sandlers paid a total of $78 for 1 adult ticket and 2 child's tickets 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.

78 = one-halfx + (x - 6)

What is the regular price of a child's ticket?
 	
	help?

anonymous · Answer

the choices are: 
A.  50

b. 56 

c. 75

d. 81

johnweldon1993 · Answer

so we have

$$\frac{ 1 }{ 2 }x + x - 6 = 78$$

We combine like terms....what is 1/2x + x?

$$\frac{ 3 }{ 2 }x - 6 = 78$$

Add 6 to both sides

$$\frac{ 3 }{ 2 }x = 84$$

And finally multiply both sides by 2/3

$$x = 84 \times \frac{ 2 }{ 3 }$$

so 84 times 2 = 168.


and 168 divided by 3 = 56 dollars for a child's admission ticket

Does that make sense?

anonymous · Answer

ohhhhhhh got the same answer! thanks! mind if i ask you one more?

anonymous · Answer

Solve the following for a and c, the regular price of an adult and child respectively.$$\left\{\frac{a}{2}+2 \frac{c}{2}=78,a-c=6\right\}$$$$\{a=56,c=50\} $$

anonymous · Answer

Solve the equation 2 over 3 k + 6 = −12 for k. Please show your work and solution in the space provided.    mind helping with one more?

johnweldon1993 · Answer

$$\frac{ 2 }{ 3k + 6 } = -12$$

like that?

anonymous · Answer

i got that toobut i feel like its to easy to be right haha

johnweldon1993 · Answer

No that is just me asking if that is the correct way the question is written?

anonymous · Answer

and also how do u do the divided sign like that on a computer?

anonymous · Answer

yea its the right set up

johnweldon1993 · Answer

Okay...so multiply both sides of the equation by 3k + 6

$$2 = -12(3k + 6)$$

Now distribute that -12 into the parenthesis...what do you get after that?

anonymous · Answer

2 = -36k - 72

johnweldon1993 · Answer

Right....so now lets add 72 to both sides to get

$$-36k = 74$$

So what does 'k' equal?

anonymous · Answer

k = 2.05

johnweldon1993 · Answer

Well I would keep it in fraction form

$$k = -\frac{ 37 }{ 18 }$$ is what I get

anonymous · Answer

why would i keep it in fraction form?

johnweldon1993 · Answer

Just makes it easier to write...

and think...when you turn this into a decimal....do you write 2.05? or 2.055? or 2.06 for rounding.....it's more exact in fraction form