The manager of a movie theater compared ticket sales for two movies showing on the same night. For the first movie, 150 adult tickets and 100 child tickets were sold for $3,087.50 in total ticket sales. For the second movie, 200 adult tickets and 150 child tickets were sold for $4,287.50 in total ticket sales. What was the price of each adult and each child ticket?

the answer is b.

step-by-step explanation:

identity property is where 0+whatever number=whatever number. basically 0+ a number.

1 x=22.52

2: 65/39=604+39x

65x-39x=604

26x=604

x=604/26

×=23.23

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

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step-by-step explanation: