Answer:
senior ticket = $10 child's ticket = $8
Step-by-step explanation:
s = senior ticket
c = child's ticket
We need to write 2 equations, and we have 2 unknowns, s and c.
3s + 5c = $70
12s + 12c = $216
First solve for s using the first equation.
3s + 5c = 70 Subtract 5c from each side
3s + 5c - 5c = 70 - 5c
3s = 70 - 5c Divide each side by 3
3s/3 = (70 - 5c)/3
s = [tex]\frac{70 - 5c}{3}[/tex]
Now plug in s into the second equation.
12s + 12c = 216
12([tex]\frac{70 - 5c}{3}[/tex]) + 12c = 216
[tex]\frac{12}{3}[/tex] (70 - 5c) + 12c = 216
4 (70 - 5c) + 12c = 216
280 - 20c + 12c = 216
280 - 8c = 216 Add 8c to each side
280 - 8c + 8c = 216 + 8c
280 = 216 + 8c Subtract 216 from each side.
280 - 216 = 216 - 216 + 8c
280 - 216 = 8c
64 = 8c Divide each side by 8
64/8 = 8c/8
64/8 = c
8 = c
Now plug c into the first equation and solve for s.
3s + 5c = 70
3s + 5(8) = 70
3s + 40 = 70 Subtract 40 from each side.
3s + 40 - 40 = 70 - 40
3s = 70 - 40
3s = 30 Divide each side by 3
3s/3 = 30/3
s = 30/3
s = 10
So a senior ticket costs $10 and a child's ticket costs $8.
