At the movie theater, child admission is $6.50 and adult admission is $9.90 On Sunday, 149 tickets were sold for a total sales of $1254.10 How many child tickets were sold that day?
Let's assume the number of child tickets sold is x.
Therefore, the number of adult tickets sold is 149 - x.
The total sales from child tickets is 6.50x.
The total sales from adult tickets is 9.90(149 - x).
Since the total sales is $1254.10, we can write the equation:
6.50x + 9.90(149 - x) = 1254.10
Expanding the equation:
6.50x + 1469.10 - 9.90x = 1254.10
Combining like terms:
-3.40x + 1469.10 = 1254.10
Subtracting 1469.10 from both sides:
-3.40x = -215
Dividing both sides by -3.40:
x = 63.24
Since we can't have a fraction of a ticket, there were 63 child tickets sold.
Graph the compound inequality on the number line. x<=3 or x>8
To graph the compound inequality x <= 3 or x > 8 on a number line, we need to plot two separate regions.
First, let's focus on x <= 3. This includes all values of x that are less than or equal to 3. We can represent this region on the number line by shading from negative infinity to 3 and including the point 3 with a closed circle.
Next, let's focus on x > 8. This includes all values of x that are greater than 8. We can represent this region on the number line by shading to the right of 8 and excluding the point 8 with an open circle.
Combining both regions, the graph of the compound inequality x <= 3 or x > 8 on the number line would look like this:
```
●----------->
-∞ -∞ -∞ -∞ -∞ -∞ -∞ 3 8
```
The shaded region would extend from negative infinity up to and including 3, and then continue from 8 to positive infinity.
Please note that the circles at 3 and 8 are included/excluded depending on whether the inequality is ≤ (closed circle) or < (open circle).
Let's assume "C" represents the number of child tickets sold and "A" represents the number of adult tickets sold.
We are given the following information:
Child admission = $6.50
Adult admission = $9.90
Total tickets sold = 149
Total sales = $1254.10
We can set up two equations to represent the given information:
1) C + A = 149 (equation 1 - representing the total number of tickets sold)
2) 6.50C + 9.90A = 1254.10 (equation 2 - representing the total sales)
To solve these two equations, we can use the substitution method or the elimination method. Let's solve using the elimination method.
First, let's multiply equation 1 by 6.5 to make the coefficients of "C" in both equations equal:
6.5 * (C + A) = 6.5 * 149
6.5C + 6.5A = 968.50 (equation 3)
Now, we can subtract equation 3 from equation 2:
(6.50C + 9.90A) - (6.5C + 6.5A) = 1254.10 - 968.50
9.90A - 6.5A = 285.60
3.40A = 285.60
A ≈ 84
Now, substitute the value of A into equation 1:
C + 84 = 149
C ≈ 149 - 84
C ≈ 65
So, approximately 65 child tickets were sold that day.
To find the number of child tickets sold, we can use a system of equations. Let's assume that 'x' represents the number of child tickets sold and 'y' represents the number of adult tickets sold.
From the given information, we know the following:
- Child admission is $6.50, so the total revenue from child tickets sold would be 6.50x dollars.
- Adult admission is $9.90, so the total revenue from adult tickets sold would be 9.90y dollars.
- On Sunday, 149 tickets were sold, so the total number of tickets sold can be represented as x + y = 149 (equation 1).
- The total sales were $1254.10, so the total revenue from tickets sold would be 6.50x + 9.90y = 1254.10 (equation 2).
Now, we have a system of equations:
x + y = 149 (equation 1)
6.50x + 9.90y = 1254.10 (equation 2)
There are multiple ways to solve this system of equations, such as substitution or elimination. Let's solve it using substitution:
From equation 1, we can isolate x and express it in terms of y:
x = 149 - y
Now substitute this expression for x in equation 2:
6.50(149 - y) + 9.90y = 1254.10
Simplify and solve for y:
971.50 - 6.50y + 9.90y = 1254.10
3.40y = 282.60
y = 83
So, the number of adult tickets sold is 83. Now substitute this value back in equation 1 to find the number of child tickets sold:
x + 83 = 149
x = 149 - 83
x = 66
Therefore, 66 child tickets were sold on Sunday.