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College Math – Age Problem

by Irish Johnson










































Word Problem - Age Problem

       Last year Fred's age was a square.

       Next year his age will be a cube.

       How old is Fred?

HINT: he is older than 21, and there are 2 years between his age that is a square and his age is that is a cube.

Comments for College Math – Age Problem

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Aug 28, 2012
Age Problem
by: Staff

Answer:

A = Fred’s age in years

We assume Fred’s age must be a whole number of years, rather than a fraction.

Last year’s age: (A – 1) = perfect square (or square number)

       A perfect square is an integer which is the square of another integer. As an example, the number 4 is a perfect square because it is the square of the integer 2. 2² = 4, a perfect square.


Next year’s age: (A + 1) = perfect cube (or cube number)

       A perfect cube is an integer which is the cube of another integer. As an example, the number 8 is a perfect cube because it is the cube of the integer 2. 2³ = 8, a perfect cube.


(A – 1) must be one of the numbers on a list of perfect squares.

Perfect squares:

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
11² = 121
12² = 144

Since A is greater than 21 (from the problems statement), (A - 1) can only be one of the following numbers:

       25, 36, 49, 64, 81, 100



(A + 1) must be one of the numbers on a list of perfect cubes.

Perfect Cubes:

1³ = 1
2³ = 8
3³ = 27
4³ = 64
5³ = 125
6³ = 216
7³ = 343
8³ = 512
9³ = 729
10³ = 1000

Since A is greater than 21 (from the problems statement), (A + 1) can only be one of the following numbers:

       27, 64, 125



According the problem statement, the difference between Fred’s age next year (A + 1) and Fred’s age last year (A – 1) is 2 years.


Fred’s age last year (A - 1) can only be: 25 (from the list of perfect squares)

Fred’s age next year (A + 1) can only be: 27 (from the list of perfect cubes)

Fred’s age next year - Fred’s age last year = 2

27 - 25 = 2 years

Solve for A, using Fred’s age next year:

(A + 1) = 27

A + 1 - 1 = 27 – 1

A + 0 = 27 – 1

A = 26


final answer

       Age = 26



Thanks for writing.

Staff
www.solving-math-problems.com



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