Help! Tickets for the senior class play cost $6 for adults and $3 for students. A total of 846 tickets worth $3,846 were sold. How many student tickets were sold? How many adult tickets were sold?

410 student and 436 adult tickets

Step-by-step explanation:

x is the number of student tickets and y is the number of adult tickets sold. we now that a total of 846 tickets were sold so x+y=846=>x=846-y. we also now that their worth was 3 846usd so 3*x+6*y=3846. we substitute x and are left with the following equation:3x+6*(846-x)=3846

5076-3x=3846

3x=1230

x=410

=>y=846-410=436

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.