Le Man had $25. After buying 3 adult tickets and 4 children tickets to a concert, she had some money left. If she used the remaining money to buy a child's ticket, she would have 50 cents left. If she used the remaining money to buy an adults children instead of a child's ticket she would be short of $1. How much did an adult ticket and a child's ticket cost?

Question

Le Man had $25. After buying 3 adult tickets and 4 children tickets to  a concert, she had some money left. If she used the remaining money to buy a child's ticket, she would have 50 cents left. If she used the remaining money to buy an adults children instead of  a child's ticket she would be short of $1. How much did an adult ticket and a child's ticket cost?

anonymous · Answer

Let the price of adult tickets be a
Let the price of children tickets be c

25 - (3a + 4c) - c = 0.5

25 - 3a - 5c = 0.5

24.5 - 5c = 3a

a =  (24.5 - 5c)/3

25 - (3a + 4c) - a = -1

25 - 4a - 4c = -1

26 = 4a + 4c

26 = 4 (24.5 - 5c)/3 + 4c

Solve for c

anonymous · Answer

c = 2.5

a = 4

anonymous · Answer

that works. you could also put 
$$25=3a+5c+.5\iff 24.5=3a+5c$$
$$25=4a+4c-1\iff 26=4a+4c$$ and solve the system