Connor went to new york for vacation. he spent 3 nights at a hotel and rented a car for 4 days. jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. if connor paid $675 and jillian paid $875, how much did one night at the hotel cost?

The cost of one night at the hotel is $125

Step-by-step explanation:

Let the cost of each night spend in hotel is = $x

Let the cost of each day of car rented = $y

Cannor spent 3 nights at a hotel and rented a car for 4 days paid $675.

 ......(1)

Jillian also spent 4 nights in same hotel and rented a car for 5 days paid $875.

 .......(2)

Now, we solve equation (1) and (2) by substitution method

From (1) take the value of x,  

then put in equation (2)

solve,

 (Taking LCM)

Now, put value of in value of  

Therefore, the cost of one night at the hotel is $125

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

4

step-by-step explanation: