# 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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### 2 Answers

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.**

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