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Question 804576: a movie theater charges php 180 for adults and php 144 for senior citizens. on day when 310 people paid an admission the otal receipts were php 54 540. how many were adults? how many were seniors?
Answer by thejackal(72)   (Show Source):
You can put this solution on YOUR website! first, you need to understand the question by writing down what you know.
so lets begin:
- the cost of a movie for an adult = 180. lets call adult A for short
- the cost of a movie for a senior = 144. lets call seniors S
- on this particular day, 310 people watched a movie but we don't know how many of them were adults or seniors. But we know for sure that 310 people were made up of A + S. A number of adults and S number of seniors.
- Now we can form our first linear equation; A + S = 310
- we also know that the receipts for this day totaled 54,540. since we know how much a ticket was for adults and seniors we can form our second equation; therefore 180A + 144S = 54,540
- we now have 2 simultaneous equations which we can solve using the substitution method.
A + S = 310
180A + 144S = 54540
1st) express S as a function of A; S = 310 - A
2nd) substitute our equation for S into equation 2; 180A + 144(310-A) = 54540
3rd) simplify;
4th) you'll find that A = 275
5th) plug A into equation 1 like so; 275 + S = 310 therefore S = 35
check your answers does 180(275) + 144(35) = 54540 ? if so you're done
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