SOLUTION: The ages of Sam, Tontom, and Ramon are consecutive integers. Sam is younger then Ramon but older than Tonton. Sam's mother is thrice as old as Sam and 14 years older than twice as

Algebra ->  Customizable Word Problem Solvers  -> Age -> SOLUTION: The ages of Sam, Tontom, and Ramon are consecutive integers. Sam is younger then Ramon but older than Tonton. Sam's mother is thrice as old as Sam and 14 years older than twice as       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1059554: The ages of Sam, Tontom, and Ramon are consecutive integers. Sam is younger then Ramon but older than Tonton. Sam's mother is thrice as old as Sam and 14 years older than twice as old as Ramon. Find the ages of each.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
S = Sam's age
T = Tonton's age
R = Ramon's age
—
ST (given)
This info implies T T=youngest age
S=T+1
R=T+2
—
Let M = mother's age
M = 3(T+1) ("Thrice as old as Sam." Recall S=T+1)
M = 2(T+2)+14 ("14 yrs older than twice as old as Ramon." Recall R=T+2)
—
Now we can solve for T (2 eqns, 2 unknowns). M is easily eliminated from the above two eqns by setting the two right hand sides equal to each other:
+3%28T%2B1%29+=+2%28T%2B2%29%2B14++
Now solve for T:
+3T+%2B+3+=+%282T%2B4%29+%2B+14+
+T+=+15+
—
Answer:
Tonton is 15
Sam is 16
Ramon is 17
—
Check (using the age relations of Sam's mother):
3*16 = 48
14+2*17 = 14+34 = 48