Gary bought a pen a book and a calculator. the book cost 2 times as much as the pen and the calculator cost $1 more than the book. he spent $16 altogether. what was the cost of the book?

A few things you're given:

b=book

p=pen

c=calculator

b + p + c = 16

Relationships in order to only use one variable:

2p=b

2p+1=c

Equation:

2p + p + 2p+1 = 16

Combining Like Terms/Simplifying and Solving:

5p + 1 = 16

5p = 15

p = 3

Remember the relationship between pen and book.

2p = b so...

2 (3) = $6.00! :)

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.