The attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened. Movie A: y=−x2+35x+100 Movie B: y=−5x+275 Where x is number of days since the movies opened. When is the attendance for each movie the same?

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The attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened.  Movie A: y=−x2+35x+100  Movie B: y=−5x+275  Where x is number of days since the movies opened.  When is the attendance for each movie the same?

Arnold Odonnell · Accepted Answer

Formula used:  x=−b±b2−4ac2a  Calculation:  Substituting value of equation 1 in equation 2,  −x2+35x+100=−5x+275  Shifting the value,  −x2+35x+100=−5x+275=0  On solving,  −x2+40x−175=0  Hence,  a=−1,  b=40,  c=−175,  Substituting the formula  x=−40±402−4(−1)(−175)2(−1)  So,  x=−40±1600−700−2  x=−40±900−2  x=−40±30−2  x=−40+30−2  x=5  Value of y, substituting in equation 2,  y=−5(5)+275  y=250  For -30,  x=−40−30−2  x=35  Value of y, substituting in equation 2,  y=−5(35)+275  y=100  Hence, x=5,35 and y=250,100  Hence, the attendance of two movies is same on day 5 and day 35

The attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened. Movie A: y=-x^{2}+35x+100 Movie B: y=-5x+275 Where x is number of days since the movies opened. When is the attendance for each movie the same?

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