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artcher [175]
2 years ago
5

Brenda's school is selling tickets to a spring musical. On the first day of ticket sales the school sold 3 senior citizen ticket

s and 1 child tickets for a total of $38. The school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. What is the price each of one senior citizen ticket ?
Senior citizen ticket: $
Mathematics
1 answer:
seropon [69]2 years ago
5 0
The answer should be $12.
Explanation:
52 - 38 = 16.
(16 is the price of a ticket for a child)
28 - 16 = 24
24 / 2 = 12
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The question is given in the picture.
lorasvet [3.4K]
This is a really interesting question! One thing that we can notice right off the bat is that each of the circles has the same amount of area swept out of it - namely, the amount swept out by one of the interior angles of the hexagon. Let’s call that interior angle θ. We know that the amount of area swept out in the circle is proportional to the angle swept out - mathematically

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Where “a” is the area swept out by θ, and A is the area of the whole circle, which, given a radius of r, is πr^2. Substituting this in, we have

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a = π(r^2)θ/360

So, we have the formula for the area of one of those sectors; all we need to do now is find θ and multiply our result by 6, since we have 6 circles. We can preempt this but just multiplying both sides of the formula by 6:

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Which simplifies to

6a = π(r^2)θ/60

Now, how do we find θ? Let’s look first at the exterior angles of a hexagon. Imagine if you were taking a walk around a hexagon. At each corner, you turn some angle and keep walking. You make 6 turns in all, and in the end, you find yourself right back at the same place you started; you turned 360 degrees in total. On a regular hexagon, you’d turn by the same angle at each corner, which means that each of the six turns is 360/6 = 60 degrees. Since each interior and exterior angle pair up to make 180 degrees (a straight line), we can simply subtract that exterior angle from 180 to find θ, obtaining an angle of 180 - 60 = 120 degrees.

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6a = π(r^2)120/60

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6a = 2πr^2

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