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The sum of the ages of Tom, Sue, and Dave is 75.  Sue is 6 years older than Tom. Dave...

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kristenmarieb... | Student, Grade 10 | (Level 1) Valedictorian

Posted February 26, 2013 at 3:31 AM via web

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The sum of the ages of Tom, Sue, and Dave is 75.  Sue is 6 years older than Tom. Dave is 15 years older than the sum of Tom and Sues age.  What are their ages? 

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samhouston | Middle School Teacher | (Level 1) Associate Educator

Posted February 26, 2013 at 4:05 AM (Answer #1)

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This problem can best be solved using a system of equations.
Let t represent Tom's age.
Let s represent Sue's age.
Let d represent Dave's age.

The sum of the ages of Tom, Sue, and Dave is 75.
Equation:     t + s + d = 75

Sue is 6 years older than Tom.
Equation:     s = 6 + t

Dave is 15 years older than the sum of Tom and Sue's ages.
Equation:     d = 15 + t + s

Substitute (6 + t) in for s in the 3rd equation.
d = 15 + t + s
d = 15 + t + (6 + t)
d = 21 + 2t

Substitute (6 + t) in for s and (21 + 2t) in for d in the 1st equation.
t + s + d = 75
t + (6 + t) + (21 + 2t) = 75

Now solve for t.
t + (6 + t) + (21 + 2t) = 75
4t + 27 = 75
4t + 27 + (-27) = 75 + (-27)
4t + 0 = 48
4t = 48
4t / 4 = 48 / 4
t = 12

Now substitute 12 in for t and solve for s and d.
s = 6 + t
s = 6 + 12
s = 18

d = 21 + 2t
d = 21 + 2 * 12
d = 21 + 24
d = 45

Tom's age is 12.  Sue's age is 18.  Dave's age is 45.

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted February 26, 2013 at 5:15 AM (Answer #2)

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T+S+D=75

S=T+6

D=T+S+15

  =T+(T+6)+15

 = 2T+21

T+(T+6)+(2T+21)=75

4T=48 ,T=12,S=12+6=18 ,D= 12+18+15=45

 

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