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BaLLatris [955]
3 years ago
7

A theater received $8,917 in ticket sales for one performance of a play. Tickets for preferred seats coast $45 each and regular

seats coast $34 each. All of the theaters 75 preferred seats were sold out that evening. How many tickets were sold?
Mathematics
1 answer:
Leya [2.2K]3 years ago
8 0
P=preferred seats
r=regular seats
45*p+34*r=8917
p=75
45*75+34r=8917
3375+34r=8917
34r=5542
r=163

All ticket sales=r+p=75+163=238
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Refer to the diagram below. We need to find the areas of the green and blue regions, then subtract to get the area of the orange track only.

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The blue area is the same story, but smaller dimensions. The blue rectangle has dimensions 200 meters by 42 meters, so its area is 200*42 = 8400 square meters. The blue semicircular pieces combine to a circle with area pi*r^2 = pi*21^2 = 441pi square meters. In total, the blue region has area 8400+441pi square meters.

After we figure out the green and blue areas, we subtract to get the orange region's area, which is the area of the track only.

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