for the school play, child tickets cost $3 and adult tickets cost $5. The number of adult tickets sold was 20 more than the number of child tickets sold. If the total sales were $2540, how many adult tickets were sold?
Let X =$ child tickets
X+20 =$ adult tickets
5(X+20) + 3X=2540
Solving for X will give you the amount in dollars sold for children tickets. Plugging the value that you obtain for X into X + 20 will give you the amount of money earned for selling adult tickets. Divide that amount from X + 20 by 5 to get the number of adult tickets sold.
65
Let's assume the number of child tickets sold as "x". According to the given information, the number of adult tickets sold is "x + 20".
The cost of each child ticket is $3, so the total revenue from child tickets can be expressed as 3x.
The cost of each adult ticket is $5, so the total revenue from adult tickets can be expressed as 5(x + 20).
The total sales revenue is $2540, so we can set up the following equation:
3x + 5(x + 20) = 2540
Now, let's solve this equation step-by-step:
3x + 5x + 100 = 2540
Combining like terms:
8x + 100 = 2540
Subtracting 100 from both sides:
8x = 2440
Dividing both sides by 8:
x = 305
Therefore, the number of child tickets sold is 305.
Since the number of adult tickets sold is 20 more than the number of child tickets sold:
x + 20 = 305 + 20 = 325
Therefore, the number of adult tickets sold is 325.
So, 325 adult tickets were sold.
To solve this question, let's assume the number of child tickets sold is "x". As given, the number of adult tickets sold is 20 more than the number of child tickets sold, so it would be "x + 20".
Now, let's calculate the revenue from the child tickets. Since each child ticket costs $3, the revenue from selling x child tickets would be 3 times x, which is 3x.
Similarly, the revenue from adult tickets can be calculated by multiplying the number of adult tickets (x + 20) by the cost of each adult ticket ($5). Therefore, the revenue from selling (x + 20) adult tickets would be 5 times (x + 20), which is 5(x + 20).
The total revenue from selling both child and adult tickets is given as $2540. So, we can set up the following equation:
3x + 5(x + 20) = 2540
Now, let's solve this equation to find the value of x, which represents the number of child tickets sold:
3x + 5x + 100 = 2540
8x + 100 = 2540
8x = 2440
x = 305
Therefore, the number of child tickets sold is 305. To find the number of adult tickets sold, we can substitute this value back into the expression we derived earlier: x + 20.
305 + 20 = 325
Hence, the number of adult tickets sold is 325.