How old is Al?

Outline Mathematics
Word Age Problems

Here's a problem to tackle:

Al's father is 45. He is 15 years older than twice Al's age. How old is Al?


Solution


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Copyright © 1996-2017 Alexander Bogomolny

Solution

Al's father is 45. He is 15 years older than twice Al's age. How old is Al?


(In the text below, some words are omitted. These have been underlined. Click just above the line. See what happens.)

The question is about Al's age. What is it? We do not know yet, but we are going to find out. Until we have, let's introduce a variable x to denote the unknown age. So, Al's age is x. What do we know about x?

We know that the number 2x which is twice Al's age is 15,10,15,20,30,45 years short of his father's age which is 45,10,15,20,30,45. So we conclude that 2x = 45 - 15 = 30,10,15,20,30,45. Divide now both sides of the equation by 2 to obtain x = 15,10,15,20,30,45. That's it.

A little more formally, we could have written an equation

  2x + 15 = 45

and tried solving it: first 2x = 45 - 15 = 30 and then again x = 15,10,15,20,30,45.

(Acknowledgement: I have lifted the problem from the Mathforum's site.)


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