At a summertime poolside snack bar, 200 ice cream scoops were sold in one day. double scoops were sold for $1.25 each and single scoops were sold for $1 each. if the proceeds from the sale of the cones were $221.75, how many of each kinds of cone were sold? in all, how many scoops of ice cream were sold?

a) 87 double scoops and 113 single scoops.

b) 287 scoops of ice cream.

Step-by-step explanation:

1. You need to make a system of equations, where double scoops are represented by and the single scoops are represented by :

2. You can apply the Elimination Method:

- Multiply the first equation by -1 to cancel the variable from the system. Add both equations:

- Solve for :

- Substitute the value of into one of the original equations and solve for :

3. You can calculate the total number of scoops of ice cream that where sold as below:

4. Substitute values:

scoops of ice cream

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.

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step-by-step explanation: