Question

The Martinez family went to the movies and paid $60 for two adult tickets and three children’s tickets. The Wright family consists of three adults and five children, the Wrights paid $95.50 when they purchased movie tickets for their family. What is the cost of an adult movie ticket?

Answer 1

a = $13.5

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;

`2a + 3c = $60` ..........equation 1

`3a + 5c = $95.5` .........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;

`2a + 3(11) = 60`

`2a + 33 = 60`

`2a = 60 - 33`

`2a = 27`

`a = (27)/(2)`

a = $13.5

Therefore, the cost of an adult movie ticket is $13.5.