The theater

The Manila theater charged ticket prices: adults php500, students php250, and children below 12 are php100. The theater collected a total of php100,000.00 from an audience of 250 people. What is a possible audience composition regarding the numbers of adults, students, and children? Write the answer with a solution.

Correct answer:

a =  186
s =  4
c =  60

Step-by-step explanation:

$$\begin{gathered} 500a+250s+100c=100000 \\ a+s+c=250 \\ {a}_1=150,c_1=0,s_1=100 \\ {a}_2=153,c_2=5,s_2=92 \\ {a}_3=156,c_3=10,s_3=84 \\ {a}_4=159,c_4=15,s_4=76 \\ {a}_5=162,c_5=20,s_5=68 \\ {a}_6=165,c_6=25,s_6=60 \\ {a}_7=168,c_7=30,s_7=52 \\ {a}_8=171,c_8=35,s_8=44 \\ {a}_9=174,c_9=40,s_9=36 \\ {a}_{10}=177,c_{10}=45,s_{10}=28 \\ {a}_{11}=180,c_{11}=50,s_{11}=20 \\ {a}_{12}=183,c_{12}=55,s_{12}=12 \\ {a}_{13}=186,c_{13}=60,s_{13}=4 \\ a=186 \end{gathered}$$

$s=4$

$c=60$

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