Question

At the movie theatre, child admission is $5.80 and adult admission is $9.70. On Tuesday, 137 tickets were sold for a total sales of S1094.90. How many adulttickets were sold that day?Number of adult tickets:?

Answer 1

Let us denote by x the number of child tickets sold and by y the number of adult tickets sold. According to the problem, we have that 137 tickets were sold, then we get the following equation:

Equation 1:

`x+y\text{ = 137}`

On the other hand, according to the problem, child admission is $5.80 and adult admission is $9.70 and the total sales were S1094.90.

Thus, we get the following equation:

Equation 2:

`5.80x\text{ + 9.70y = }1094.90`

Thus, we get the following system of linear equations:

Equation 1:

`x+y\text{ = 137}`

Equation 2:

`5.80x\text{ + 9.70y = }1094.90`

Now, solving for x, the equation 1, we get:

Equation 3:

`x=\text{ 137-y}`

replacing this into equation 2, we obtain:

`5.80(137-y)\text{ + 9.70y = }1094.90`

now, applying the distributive property, we get:

`794.6-5.80y\text{ + 9.70y = }1094.90`

this is equivalent to:

`-5.80y\text{ + 9.70y = }1094.90-794.6`

this is equivalent to:

`3.90y=300.3`

solving for y, we get:

`y=(300.3)/(3.90)=77`

Now, replacing this data into equation 3, we obtain:

`x=\text{ 137-y}=137-77=60`

So that, we can conclude that the correct answer is:

the number of child tickets sold = x = 60

the number of adult tickets sold = y = 77