Paul Linda and Aaron make handmade cards. Paul can make one card for every three cards Linda makes. Linda can make three cards for every two cards that Aaron makes. During a week Aaron makes 72 cards. How many more cards does Linda make those Paul during this week?

Linda makes 3 more cards for every 1 card that Paul makes

Step-by-step explanation:

Paul can make one card for every three cards Linda makes.

Paul : Linda = 1 : 3

P/L = 1/3

3P = L (1)

Linda can make three cards for every two cards that Aaron makes.

Linda : Aaron = 3 : 2

L/A = 3/2

2L = 3A (2)

During a week Aaron makes 72 cards. How many more cards does Linda make those Paul during this week?

From (2)

L = 3/2A

A = 72

L = 3/2*72

= (3*73) / 3

= 216/2

= 108

Linda = 108

From (1)

P = 1/3L

= 1/3*108

= (1*108) / 3

= 108/3

= 36

Paul = 36

Finally, the number of cards that Linda makes more than Paul is:

Linda : Paul = 108 : 36

= 108/36

= 3/1

Linda : Paul = 3 : 1

Therefore, Linda makes 3 more cards for every 1 card that Paul makes

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.

typically if you want , you would actually put questions here for us to you. but hey, that's just me. maybe someone will magically answer the questions for you without knowing what they are.