A movie theater offers two options for membership. The first option costs $15 per ticket but an initial fee of $10. The second option costs $10 per ticket but an initial fee of $45. After how many tickets are both options the same price? Click Here for Help Video(1 point)
Two pumps are being filled by two different pumps. The first vat has 10 gallons is being filled at a rate of 12 gallons per second. The second vat has 25 gallons and is being filled at a rate of 10 gallons per second. After how many seconds will both vats have the same amount of liquid? Click Here for Help Video(1 point)
A movie theater offers a special pricing for membership. The normal cost is $7.50 per ticket. The membership costs $5 per ticket but an initial fee of $25. After how many tickets are both options the same price? Click Here for Help Video
There are two different vats. The first vat has 12 gallons is being filled at a rate of 3 gallons per minute. The second vat has 108 gallons and is leaking fluid at a rate of 7 gallons per minute. After how many seconds will both vats have the same amount of liquid? Click Here for Help Video(1 point)
omg bro that s wrong
To determine the number of tickets at which both options are the same price, we need to set up an equation.
Let's denote the number of tickets as "x."
For the first option, the cost of x tickets would be: $15x + $10 (initial fee).
For the second option, the cost of x tickets would be: $10x + $45 (initial fee).
We need to find the value of x when both options have the same cost.
So, we can set up the equation:
$15x + $10 = $10x + $45
Now, let's solve this equation for x.
$15x - $10x = $45 - $10
$5x = $35
Dividing both sides by 5:
x = $35 / $5
x = 7
Therefore, after purchasing 7 tickets, both membership options will have the same price.
Let's represent the number of tickets as x.
For the first option, the total cost is given by the equation:
Cost = (15 * x) + 10
For the second option, the total cost is given by the equation:
Cost = (10 * x) + 45
Now we set these two equations equal to each other to find when the options have the same price:
(15 * x) + 10 = (10 * x) + 45
Subtracting 10x from both sides:
5 * x + 10 = 45
Subtracting 10 from both sides:
5 * x = 35
Dividing both sides by 5:
x = 7
Therefore, both options will have the same price after 7 tickets.
Let's represent the number of seconds as x.
For the first vat, the total amount of liquid is given by the equation:
Amount = 10 + 12x
For the second vat, the total amount of liquid is given by the equation:
Amount = 25 + 10x
Now we set these two equations equal to each other to find when the vats have the same amount of liquid:
10 + 12x = 25 + 10x
Subtracting 10x from both sides:
2x = 15
Dividing both sides by 2:
x = 7.5
Therefore, both vats will have the same amount of liquid after 7.5 seconds.
Let's represent the number of tickets as x.
For the normal pricing option, the total cost is given by the equation:
Cost = 7.50 * x
For the membership pricing option, the total cost is given by the equation:
Cost = 5 * x + 25
Now we set these two equations equal to each other to find when both options have the same price:
7.50x = 5x + 25
Subtracting 5x from both sides:
2.5x = 25
Dividing both sides by 2.5:
x = 10
Therefore, both options will have the same price after 10 tickets.
Let's represent the number of seconds as x.
For the first vat, the total amount of liquid is given by the equation:
Amount = 12 + (3/60)x
For the second vat, the total amount of liquid is given by the equation:
Amount = 108 - (7/60)x
Now we set these two equations equal to each other to find when the vats have the same amount of liquid:
12 + (3/60)x = 108 - (7/60)x
Multiplying both sides by 60 to get rid of the fractions:
720 + 3x = 6480 - 7x
Adding 7x to both sides:
10x + 720 = 6480
Subtracting 720 from both sides:
10x = 5760
Dividing both sides by 10:
x = 576
Therefore, both vats will have the same amount of liquid after 576 seconds.
Apologies for the mistake. Let's correct it:
For the first vat, the total amount of liquid is given by the equation:
Amount = 12 + (3/60)*x
For the second vat, the total amount of liquid is given by the equation:
Amount = 108 - (7/60)*x
Now we set these two equations equal to each other to find when the vats have the same amount of liquid:
12 + (3/60)*x = 108 - (7/60)*x
Multiplying both sides by 60 to get rid of the fractions:
720 + 3x = 6480 - 7x
Adding 7x to both sides:
10x + 720 = 6480
Subtracting 720 from both sides:
10x = 5760
Dividing both sides by 10:
x = 576
Therefore, both vats will have the same amount of liquid after 576 seconds.