Answer:
12
Step-by-step explanation: 18/3=6 6(2)= 12
b = number of tickets sold before
a = number of tickets sold after
cost of a ticket = number of tickets times cost per ticket
before cost = 39.95b
after cost = 54.95a
total cost = 925000
39.95b + 54.95a = 925000
total number tickets = 20000
b + a = 20000
we have
39.95b + 54.95a = 925000
b + a = 20000
multiply second equation by -39.95 and add to first equation
39.95b + 54.95a = 925000
-39.95b-39.95a = -799000 +
0b+15a = 126000
15a = 126000
divide bot sides by 15
a = 8400
sub back
b + a = 20000
b+8400 = 20000
minus 8400 both sides
b = 11600
11,600 tickets sold before
8400 tickets sold after
Newton's law of cooling says the rate of change of temperature is proportional to the difference between the object's temperature and the temperature of the environment.
Here, the object starts out at 200 °F, which is 133 °F greater than the environment temperature. 10 minutes later, the object is 195 °F, so is 128 °F greater than the environment. In other words, the temperature difference has decayed by a factor of 128/133 in 10 minutes.
The solution to the differential equation described by Newton's Law of Cooling can be written as the equation
T(t) = 67 + 133*(128/133)^(t/10)
where T is the object's temperature in °F and t is the time in minutes from when the object was placed in the 67 °F environment.
The equation
T(t) = 180
can be solved analytically, but it can be a bit easier to solve it graphically. A graphing calculator shows it takes
42.528 minutes for the temperature of the coffee to reach 180 °F.