## Word Problems: Age Related

The majority of age problems include the present ages of two or more persons, in addition to their ages at particular past and/or future times. The key to solving these problems is to translate the verbiage into equations using subscripted variables.

Example #1:

Brian is presently four times older than Sam. Six years later, he will be twice as old as Sam. How old are Brian and Sam?

Solution #1:

Using subscripts variables of B

_{P}and S

_{P}to denote the age of Brian and Sam at the present time, we may construct the following table:

Present Age | Age Six Years Later | |

Brian | B_{P} |
B_{P} + 6 |

Sam | S_{P} |
S_{P} + 6 |

Since Brian is presently four times the age of Sam:

B

_{P}= 4S

_{P}

Knowing that Brian will be twice as old as Sam in six years:

B

_{P}+ 6 = 2(S

_{P}+ 6)

Substituting B

_{P}= 4S

_{P}:

4S

_{P}+ 6 = 2(S

_{P}+ 6)

4S

_{P}+ 6 = 2S

_{P}+ 12

4S

_{P}− 2S

_{P}= 12 − 6

2S

_{P}= 6

S

_{P}= 3 years old

Since B

_{P}= 4S

_{P}:

B

_{P}= 4(3) Years Old

B

_{P}= 12 years old

Example #2:

A year ago, John was three times as old as Larry. A year later, he was twice as old as Larry. How old are John and Larry?

Solution #2:

Using subscripts variables of J

_{P}and L

_{P}to denote the age of Brian and Sam at the present time, we may construct the following table:

Present Age | Age Year Ago | Ago Year Later | |

John | J_{P} |
J_{P} − 1 |
J_{P} + 1 |

Larry | L_{P} |
L_{P} − 1 |
L_{P} + 1 |

Since John was three times as old as Larry a year ago:

J

_{P}− 1 = 3(L

_{P}− 1)

J

_{P}− 1 = 3L

_{P}− 3

J

_{P}= 3L

_{P}− 2

Knowing that John will be twice as old as Brian in one year:

J

_{P}+ 1 = 2(L

_{P}+ 1)

Substituting J

_{P}= 3L

_{P}− 2

_{}:

(3L

_{P}− 2) + 1 = 2(L

_{P}+ 1)

3L

_{P}− 1 = 2L

_{P}+ 2

3L

_{P}− 2L

_{P}= 2 + 1

L

_{P}= 3 years old

Since J

_{P}= 3L

_{P}− 2

_{}:

J

_{P}= 3L

_{P}− 2

J

_{P}= 3(3)

_{}− 2 years old

B

_{P}= 7 years old

Related Topics:

- Consecutive Integer Word Problems
- Direct Variation Word Problems
- Inverse Variation Word Problems
- Ideal Gas Law Word Problems
- Age Word Problems