SOLUTION: There were 144 tickets sold for a movie. The ratio of the number of child tickets to the number of adult tickets to the number of senior tickets was 4 : 7 : 1. How many of each ty

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Question 703303: There were 144 tickets sold for a movie. The ratio of the number of child tickets to the number of adult tickets to the number of senior tickets was 4 : 7 : 1. How many of each type of ticket were sold? (2 points)
44 child tickets, 77 adult tickets, and 11 senior tickets
48 child tickets, 84 adult tickets, and 12 senior tickets
60 child tickets, 80 adult tickets, and 4 senior tickets
59 child tickets, 77 adult tickets, and 8 senior tickets
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +c+ = number of Child's tickets
Let +a+ = number of adult tickets
Let +s+ = number of senior tickets
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(1) +c%2Fa+=+4%2F7+
(2) +a%2Fs+=+7%2F1+
(3) +c%2Fs+=+4%2F1+
(4) +c+%2B+a+%2B+s+=+144+
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(1) +c+=+%284%2F7%29%2Aa+
(2) +s+=+%281%2F7%29%2Aa+
Substitute these results into (4)
(4) +c+%2B+a+%2B+s+=+144+
(4) +%284%2F7%29%2Aa+%2B+a+%2B+%281%2F7%29%2Aa+=+144+
(4) +%2812%2F7%29%2Aa++=+144+
(4) +a+=+%287%2F12%29%2A144+
(4) +a+=+84+
and
(1) +c+=+%284%2F7%29%2Aa+
(1) +c+=+%284%2F7%29%2A84+
(1) +c+=+48+
and
(2) +s+=+%281%2F7%29%2Aa+
(2) +s+=+%281%2F7%29%2A84+
(2) +s+=+12+
48 child , 84 adult, 12 senior tickets