How old is each person?

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?

Answer 1

Hi Deklin,

 

We need to establish a few variables.

If we let Mrs West be "w" and her aunt be "a", then we can translate each sentence into math.

 

"Mrs West is 14 years younger than her aunt":  w=a-14

"Mrs West's age in years is as much below 60 as her aunt's age is over 40".

 

So we may need a variable for the difference in the 2nd sentence.  So let's use "d" for this difference.

 

"Mrs. West's age in years is as much below 60":  w=60-d

"as her aunt's age is over 40": a=40+d

 

 

So now we have 3 equations and 3 unknowns:

 

w=60-d

a=40+d

w=a-14

 

Putting variables in same order on left, we get

 

     d + w = 60

a - d       = 40

a       - w = 14

 

Can eliminate both d and w if we vertically add all three equations.

 

2a = 0d + 0w = 114

 

so a = 114/2

 

a=57

 

So Mrs. West's aunt is 57 years old.

Mrs. West is 14 years younger than her aunt, so she is (57-14) = 43 years old.

 

Now check:  Mrs. West aunt's age is 17 years over 40

Mrs West's age is 60-17=43  is the same number of years under 60.  So it looks like we got the right answer!