Answer:
a = $13.5
Step-by-step explanation:
Let a = adult tickets
Let c = children tickets
Translating the word problem into an algebraic equation;
For the Martinez family;
2a + 3c = $60
For the Wright family;
3a + 5c = $95.5
Thus, the simultaneous equations are;
[tex] 2a + 3c = $60[/tex] ..........equation 1
[tex] 3a + 5c = $95.5[/tex] .........equation 2
We would use substitution method to solve;
From equation 2, we make a the subject of formula;
3a = 95.5 - 5c
a = (95.5 - 5c)/3
Substituting the value of "a" into equation 1, we have;
2[(95.5-5c)/3] + 3c = 60
Multiplying all through by 3;
2(95.5 - 5c) + 9c = 180
191 - 10c + 9c = 180
191 - c = 180
c = 191-180
c = $11
To find the value of a;
2a +3c = 60
Substituting the value of "c" into the equation, we have;
[tex] 2a + 3(11) = 60[/tex]
[tex] 2a + 33 = 60[/tex]
[tex] 2a = 60 - 33[/tex]
[tex] 2a = 27[/tex]
[tex] a = \frac{27}{2}[/tex]
a = $13.5
Therefore, the cost of an adult movie ticket is $13.5.
