If two adults and three children go to the movies, it costs $31.50. If one adult and five children go to the movies, it costs $35.00. What is the cost of one adult movie ticket?

Question

anonymous · Answer

$$2a+3c=31.50$$$$a+5c=35.00$$
Lets solve for a in the second equation since it seems to be the least complicated.$$a+5c=35$$$$a=35-5c$$ Now that we know the value of a in terms of c we can solve for c. $$2(35-5c)+3c=31.50$$$$70-10c+3c=31.50$$$$70-7c=31.50$$$$7c=-38.5$$$$c=-5.50$$ Now that we know the price of a children's ticket, we can calculate the amount of an adult's ticket by plugging 5.50 into one of the equations and solving for a. $$a+5(5.50)=35$$$$a+27.50=35$$$$a=35-27.5$$$$a=7.50$$Now we'll double check that answer by plugging it into the first equation. $$2(7.50)+3(5.50)=31.50$$ $$15+16.5=31.50$$$$31.50=31.50$$ Check. So an adult ticket costs $7.50.