Store a sells 5 ballpoint pens for $2.45. what is the least number of pens store b must offer for $5.00 to beat store a's price?

a 9
b 10
c 11
d 12

plz anwser

The answer would be C: 11. Here’s why:

The price of each pen at Store A would be 49¢. ($2.45 divided by 5).

The price of each pen from store B for each of the answer choices is as follows:

A: About 55¢

B: 50¢

C: About 45¢

D: About 42¢

If they want to beat Store A’s deal with the least amount of pens involved, then choice C is the best option.

picture below

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.