So, if Dylan has x dollars and he bought 3 tickets with them, the tickets were priced at k dollars per ticket. If he bought 5 tickets with the x dollars and saved 12 total dollars, it would be the same as buying the tickets with x-12 dollars, so we have:
[tex] \frac{x}{3}=k\\
\frac{x-12}{5}=q [/tex]
So, with this we have:
[tex] x=3k\\
x=5q+12 [/tex]
If we're looking for a number that satisfies these constraints, we can work with modular arithmetic. We have:
[tex] x\equiv 0 \pmod{3}\\
x\equiv 12 \pmod{5} [/tex]
So, we can use the chinese remainder theorem here. So, we clearly have x=3k, which means:
[tex] 3k\equiv12 \pmod{5} \implies\\
k \equiv 4 \pmod{5} \implies\\
k=5j+4
[/tex]
So, since we have x=3k, we also have x=3(5j+4)=15j+12.
So, clearly j=0 won't work so we should have j=1. That means our money per ticket for the five tickets is:
[tex] \frac{27-12}{5}=3 [/tex]
And our money per three tickets is:
[tex] \frac{27}{3}=9 [/tex]
This is easily verifiable. Three tickets needs 27 dollars and 5 tickets needs 15 dollars, which is 12 less than 27 dollars. So we have our money per three dollar ticket at 6 more than money per five dollar.
Answer:
$2.40
Step-by-step explanation:
cost originally=x/3
5 tickets=5x/3-12
so
(x/3)-(1/5)((5x/3)-12)=x/3-x/3+12/5
We get 12/5 which equals 2.40
