How would I solve this problem?

Question

Mrs. West is 14 years younger than her aunt. If Mrs. West's age in years is as much below 60 as her aunt's age is over 40, how old is each?

 

I can understand the first sentence and end up getting this:

 

Let x = age of her aunt today
x-14 = age of mrs. west

 

but the wording on sentence two is very much confusing me. I hope someone can help.

 

Edit: Someone else also uploaded this same problem, but no clear answer was given for the second part. I am not the type to copy answers, I just need someone to show me how to do this specific type of problem so I can commit it to memory.

Answer 1

Using the two equations you provide:

 

60 - (x - 14) represents how much younger than 60 West is

x - 40 represents how much older than 40 the aunt is

 

These two are equal

 

60 - (x - 14) = x - 40

60 - x + 14 = x - 40      distribute

74 - x = x - 40              combine like terms

74 = 2x - 40                 add x to both sides

114 = 2x                      add 40 to both sides

57 = x                         divide both sides by 2

 

The aunt is fifty-seven and Mrs. West is forty-three.

Answer 2

"Let x = age of her aunt today
x-14 = age of mrs. west"
Good so far!  
 
In word (story) problems, each word or phrase is translated to a math symbol or expression.  Make a "translation dictionary" of these and add to it with every problem:
      is           means         =
   younger                       -
 as much below               -
 as much above              -
    as...is                        =
 
"Mrs. West's age in years is as much below 60 as her aunt's age is over 40"
                                                        60 - (x-14)                  =    (x) - 40
 
60 - (x-14) = x - 40             [re-write]
60 - x + 14 = x - 40             [distribute (-1)]
 74 - x = x - 40
   -2x = -114                     [subtract x and subtract 74 from both sides]
     x = 57                      [divide both sides by -2]
  and x-14 = 43

Checking (here's where you gain confidence!):
  Is   60 - 43 =  57 - 40   ?

           17    =   17   ?yes