# Algabra

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

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1. H < D < T

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

3 D = 2 T + 13

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

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2. D = '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:

's mother is three times as old as :

M = 3 D = 3 * 17 = 51 yrs

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

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

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