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 = x + (x - 6)

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

$50

$56

$75

$81

Answer 1

i think 56

Answer 2

Should be $50. Did you copy down the equation correctly to account for half off?

Answer 3

Regularly: c = a-6 and a = a
But this is during the off-peak season, so everything is half off:

c = (a-6)/2 and a = a/2

So the equation for off-peak is:

78 = (a/2) + 2((a-6)/2) {the two 2s on the right side of the plus sign will cancel each other out}

78 = (a/2) + (a - 6)

Remove parentheses through distributing and then add 6 to both sides:

84 = a/2 + a

84 = a(1/2 + 1)

84 = a(1.5)

Divide both sides by 1.5

a = 56 which is the adult ticket price.

Subtract 6 from that to get the child's ticket price: $50.

Answer 4

This part may be confusing:
84 = a/2 + a
84 = a(1/2 + 1)

Basically:

84 = a/2 + a is the same thing as
84 = (1/2)a + (1)a
or
84 = (1.5)a

Answer 5

Hope that helped and don't forget to mark a Best Response. Take care!