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olchik [2.2K]
3 years ago
9

Mark has been watching 16 movies for the past x months. Max has been trying to keep up with his pace but has only been able to w

atch half as many as Mark has. Between the two of them, they have watched a total of 144 movies. For how many months have they been watching 144 movies?
A. 3
B. 4
C. 5
D. 6
Mathematics
1 answer:
egoroff_w [7]3 years ago
4 0

Mark = 16

Max = 8

16 + 8 = 24

144/24 = 6

Option D. 6 months

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Step-by-step explanation:

Given\ (8x+3k)(9x-2)=0\\\\Product\ of\ two\ expressions\ is\ zero\ then\ one\ of\ them\ must\ be\ zero.\\\\If\ (9x-2)=0\\\\Add\ 2\ both\ the\ sides\\\\9x-2+2=0+2\\\\9x=2\\\\divide\ both\ sides\ by\ 9.\\\\\frac{9x}{9}=\frac{2}{9}\\\\x=\frac{2}{9}\\\\When\ (8x+3k)=0\\\\8x=-3k\\\\x=\frac{-3k}{8}\\\\

Solutions\ are\ \frac{2}{9}\ and\ \frac{-3k}{8}\\\\Product\ of\ these\ solutions=-3\\\\\frac{2}{9}\times \frac{-3k}{8}=-3\\\\-\frac{6k}{72}=-3\\\\\frac{2k}{72}=1\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ divide\ both\ sides\ by\ -3\\\\k=\frac{72}{2}=36

Other Method:

Product of solutions: Product of the roots of the polynomial ax^2+bx+c=0 is given by \frac{c}{a}

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