CPhill

Let F be the number of friends and S be the total number of  stamps.....we have these equations :

S - 2F  = 6   

S - 3F  = -1       ("short 1" means  negative 1 )

Multiply the first equation by 3  and the second equation by -2

3S - 6F  = 18

-2S +6F =  2       add these

S  =  20

So.....he has 20 stamps  and he has   20 - 2F = 6   →  2F = 20 - 6 →  2F = 14  →  7 friends

Let P be the  true price of  one pair of these shoes and let M be the amount of money he has 

So   we have these  equations :

11P =    M + 145      →   M = 11P - 145      (1)

8P =      M - 182      →    M = 8P + 182      (2)

Equate (1) and (2)

11P - 145  = 8P + 182     rearrange as

11P - 8P =  182 + 145

3P = 327

P = 327/3 =  $109  = the price of one pair

So 11 pair cost   11*109  =  $1199

2%  = .02

Let the fat content in whole milk be x

And 50% of this =  .50x

So

x  - .50x  = .02

.50x = .02

x = .02/.50 = .04 =   4%   = 4/100 = 1/25   (fat content in  whole milk )

Good job, plaintainmountain !!!!!

Let the smaller digit =  d

Let the larger digit = 2d - 1

So the larger number can be expressed as  10(2d-1) + d

And the smaller number can be expressed as 10d + 2d -1

And the difference  between these = 36 .....so......

[10(2d -1) + d]  - [ 10d + 2d -1] =  36          simplify

20d -10 + d - 10d -2d + 1  = 36

9d - 9 = 36

9d = 36 + 9

9d =45

d = 45/9 = 5

2d -1  =  9

Her favorite number =  95   and the other is 59  and their difference = 36

"e" is NOT an "imaginary" number....  is the  base for the  natural logarithm  (just as 10 is the base  for the  "normal" log)

It equals  ≈ 2.71828.....   (it is irrational so it has a non-repeating, non-terminating decimal part )

This number  comes in very handy for many scientific and financial applications  (such as growth/decay functions)

Textot provides a nice solution here :

https://web2.0calc.com/questions/terminating-decimals_4

Call the original  amount in his savings, S

Amt he spent on the watch =  (1/4)(3/5)S = (3/20)S

He has (3/5)S - (3/20)S =  (9/20)S   left

Amt he spent on the DVD player =  (5/6) ( 9/20)S =  (9/24)S

So

(3/5)S - amt on watch - amt on DVD player  = 30           ......in equation form......

(3/5)S -  (3/20)S - (9/24)S = 30

[ 72 - 18 - 45 ] / 120 S   = 30

[ 9] /120 S  =  30

S = (120 * 30) / 9 =  $400 = amt of original savings

Amt spent on watch = (3/20)(400)  =   $60

This is known as a "see-saw" problem

3 *2  =  5 * x            where x is the  time in hours for 5 people to cut the property

6 =  5 * x                divide both sides by 5

6/5  = x

It will take 5 people 6/5 of an hour to  cut the property = 1 + 1/5 hrs =  =  1 hr  12 min

If his mean score was 91 on two tests....his  combined  score  must have been  91 * 2  =  182