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Age Word Problem - Math

by Wendy
(Elkhart)










































a colonel spent 1/4 fo his life as a boy, 1/5 of his life as a young man, 1/3 of his life as a responsible adult, and 13 years on a pension. How old was he when he died?

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Mar 29, 2012
Age Word Problem
by: Staff

Question:

by Wendy
(Elkhart)


a colonel spent 1/4 of his life as a boy, 1/5 of his life as a young man, 1/3 of his life as a responsible adult, and 13 years on a pension. How old was he when he died?


Answer:

A = age at death

years of life as a boy = (1/4)*A

years of life as a young man = (1/5)*A

years of life as a responsible adult = (1/3)*A

years of life on a pension = 13



A = (years of life as a boy) + (years of life as a young man) + (years of life as a responsible adult) + (years of life on a pension)

The equation which needs to be solved:

A = (1/4)*A + (1/5)*A + (1/3)*A + 13


Solve for A

A = (1/4)*A + (1/5)*A + (1/3)*A + 13

A = (15/60)*A + (12/60)*A + (20/60)*A + 13

A = (47/60)*A + 13

A - (47/60)*A = (47/60)*A + 13 - (47/60)*A

A - (47/60)*A = (47/60)*A - (47/60)*A + 13

A - (47/60)*A = 0 + 13

A - (47/60)*A = 13

(13/60)*A = 13

(60/13)*(13/60)*A = (60/13)*13

(60/60)*(13/13)*A = (60/13)*13

(1)*(1)*A = (60/13)*13

A = (60/13)*13

A = (60)*(13/13)

A = (60)*(1)

A = 60

>>> the final answer: A = 60 years

---------------------------------------------

Check the answer by substituting 60 for every “A” in the original equation.

A = (1/4)*A + (1/5)*A + (1/3)*A + 13

60 = (1/4)*60 + (1/5)*60 + (1/3)*60 + 13

60 = 15 + 12 + 20 + 13

60 = 60, OK → A = 60 is a valid solution





Thanks for writing.

Staff
www.solving-math-problems.com



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