SOLUTION: Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill?

Question 1091701: Tom is 2 years older than Sue and Bill is twice as old as Tom.
If you add all their ages and subtract 2, the sum is 20.
How old is Bill?
Answer by Edwin McCravy(20059) (Show Source): You can put this solution on YOUR website!
>>Tom is 2 years older than Sue<<

T = S+2            <--first equation

>>and Bill is twice as old as Tom.<<

B = 2T               <--second equation

>>If you add all their ages and subtract 2, the sum is 20.<<

T + S + B - 2 = 20   <--third equation

Use the first equation to substitute (S+2) for T in the second equation.

B = 2(S+2)     <--fourth equation

Use the first equation to substitute S+2 for T in the third equation.
Use the fourth equation to substitute 2(S+2) for B in the third equation

  T   + S +    B   - 2 = 20   <--third equation
(S+2) + S + 2(S+2) - 2 = 20
S + 2 + S + 2S + 4 - 2 = 20
                4S + 4 = 20
                    4S = 16
                     S = 4, so Sue is 4 years old.

Substitute 4 for S in the first equation:

T = S+2            <--first equation
T = 4+2
T = 6, so Tom is 6 years old.

Substitute 6 for T in the second equation:

B = 2T             <--second equation
B = 2(6)
B = 12, so Bill is 12 years old.

How old is Bill?

Bill is 12 years old.

Edwin

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