Shawna has $100 in the bank. she deposits $5 each week. ruben has $75 in the bank. he deposits $20 every monday, and he spends $10 each week. after how many weeks will they have the same amount in the bank? show or explain how you got your answer.

Set up 2 equations, with x being the number of weeks:

Shawna = 100 + 5x

Ruben = 75 + 10x ( Use 10 because although he deposits 20 he uses 10, so every week his account only increases by 10).

Set the equations equal to each other and solve for x:

100 + 5x = 75 + 10x

Subtract 5x from both sides:

100 = 75 + 5x

Subtract 75 from both sides:

25 = 5x

Divide both sides by 5:

x = 25/5

X = 5

It will take 5 weeks.

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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