Aaron, Ben and Caleb all have grabbed some lollies from a jar. Ben has twice as many lollies as Aaron, and Caleb has 5 more lollies than Ben. If there are 65 lollies
altogether, how many does each have?
(create an equation and then solve it, allow Aaron to represent a lollies)

Step-by-step explanation:

So, to start off with, find all of the variables in the equation.

Aaron: x

Ben: 2x

C: (5 + 2x)

65 is how many lollies we they have altogether.

So now we start to make the equation.

x + 2x + 5 + 2x = 65.

Add like terms.

5x + 5 = 65.

65 - 5 = 60

5x = 60

60/5 = 12

Aaron = 12 lollies

Now find the amount of bens lollies

2(12) = 24

Ben = 24 lollies

24 + 5 = 29

Caleb = 29 lollies.

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.

by definition, an arc subtended by a central angle of some given measure has the same measure. so .