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

Solution:

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:

$y=\frac{300.3}{3.90}=77$

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