SOLUTION: Mary's age is twice Tom's age and one-third of Sally's age. If the sum of their ages is 99, how old is Mary? I feel like this is so easy, but I'm obviously missing something becau

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Question 170711: Mary's age is twice Tom's age and one-third of Sally's age. If the sum of their ages is 99, how old is Mary?
I feel like this is so easy, but I'm obviously missing something because I can't get the correct answer. Thank you.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
these can be confusing at times. One must first find what is missing....we need Mary's ,Tom's, and Sally's ages, which we will call m,t,and s respectively.
:
so we have 3 unknowns:so lets see if we can come up with 3 equations
:
m=2t............eq 1
m=(1/3)s..........eq 2
m+t+s=99........eq 3
:
lets rewrite eq 2 in terms of s and t by plugging in m's value from eq 1 into eq 2 (2t)=(1/3)s
multiply terms by 3---->6t=s---> now we have m(eq 1) and s(eq 2) in terms of t.
:
so take m's value in eq 1 and s's re written value from eq 2 and plug them into eq 3
:
2t+t+6t=99
:
9t=99
:
highlight%28t=11%29toms age
:
from eq 1highlight%28m=2%2811%29=22%29 mary's age
:
from eq 2highlight%28s=6%2811%29=66%29 sally's age