Sam is twice as old as Mary and Mary is 5 years older than her sister Kate. The sum of all their ages is 31.

Question

Sam is twice as old as Mary and Mary is 5 years older than her sister Kate. The sum of all their ages
is 31. Find the age of:
Kate =
Mary =
Sam =

Answer 1

s = Sam's age

m = Mary's age

k = Kate's age

 

s = 2m

m = k+5 , therefore,   k = m-5

s+m+k = 31

 

In 3rd equation replace s with 2m; replace k with m-5; solve for m

 

2m + m + m-5 = 31

4m-5 = 31

 

Finish solving for m to get Mary's age.

Then use k = m-5 and s = 2m to find Kate and Sam's ages.