Question

Dick is younger than Tom, but older than Harry. Their ages in years are consecutive odd integers. Dick's mother is three times as old as Dick, and she is also 13 years older than twice as old as Tom. How old are Harry, Dick, and Tom

Answer 1

H < D < T

H + 2 = D ... D + 2 = T

3 D = 2 T + 13

3 D = 2 (D + 2) + 13 = 2 D + 17

Answer 2

D = Dick's age

T = Tom's age

H = Harry's age

M = Mother's age


D < T

D > H


D = T - 2 Add 2 to both sides

D + 2 = T - 2 + 2

D + 2 = T

T = D + 2


M = 3 D

also:

M = 2 T + 13 = 2 ( D + 2 ) + 13 = 2 * D + 2 * 2 + 13 = 2 D + 4 + 13 = 2 D + 17


M = M

3 D = 2 D + 17 Subtract 2 D to both sides

3 D - 2 D = 2 D + 17 - 2 D

D = 17 yrs

T = D + 2 = 17 + 2 = 19 yrs

D = H + 2 Subtract 2 to both sides

D - 2 = H + 2 - 2

D - 2 = H

H = D - 2

H = 17 - 2 = 15 yrs


Proof:

Dick's mother is three times as old as Dick:

M = 3 D = 3 * 17 = 51 yrs

Dick's mother is 13 years older than twice as old as Tom:

M = 2 T + 13 = 2 * 19 + 13 = 38 + 13 = 51 yrs