How to Solve Age Problems Part 2

This is the second part of the Solving Age Problem Series. We will continue solving age problems that are slightly more complicated that the first part. We have already discussed 3 problems in the first part of this series, so we continue with the fourth problem.

Problem 4

Simon is four years older than Jim. The sum of their ages is 52. How old is Simon?

Scratch Work

This problem is a sort of review of first part of this series. Simon is older than Jim by 4 years. So, if Jim is x years old, then Simon is x + 4 years old. The sum of their ages is 52. This means that if add x and x + 4, then the sum is 52. That is the equation.

Solution

Let x be Jim’s age and x + 4 be Simon’s age.

Now,

Jim’s age + Simon’s age = 52 which means that

x + (x + 4) = 52.

Simplifying we have

2x + 4 = 52.

Subtracting 4 from both sides, we have

2x = 48

x = 24

So, Jim is 24 years old. Now, the question asks for the age of Simon. Simon is 24 + 4 = 28 years old.

Check

Simon is 28 and Jim is 24, so he is indeed four years older. The sum of their ages is 28 + 24 = 52 which agrees with the given in the problem. Therefore, we are correct.

Problem 5

Allan is 5 times as old as Leah. Five years from now, he will be 3 times as old. How old is Allan?

Scratch Work

Now, if Leah is, for example, 7 years old, then Allan is 5(7) years old. This means that if Leah is x years old, then Allan is 5x years old. Five years from now, Leah will be x + 5 years old and Allan will be 5x + 5 years old as shown on the table below.

Screen Shot 2014-03-21 at 12.55.04 PM

 

Note that $latex $5 years from now, Allan will be three times as old as Leah. This means that if we multiply Leah’s age by 3, then, their ages will be equal. That is, if we multiply x + 5 by 3, it will be equal to 5x + 5. In equation form,

3(x + 5) = 5x + 5

which is the final equation.

Solution

Let x be Leah’s age and 5x be Allan’s age.

Five years from now, Leah will be x + 5 years old and Allan will be 5x + 5 years old.

Now, we multiply Leah’s age and equate it to that of Allan’s

3(x + 5) = 5x + 5.

By Distributive Property, we have

3x + 15 = 5x + 5.

Putting all x’s to the right and all numbers to the left, we have

15 - 5 = 5x - 3x

10 = 2x.

Dividing both sides by 2, we have

5 = x.

So, Leah is 5 years old and Allan is 5(5) = 25

Check

Allan is 25 and Leah is 5 so he is indeed 5 times as old. In 5 years, Allan will be 30 and Leah will be 10. Thirty is indeed three times 10, so we are correct.

Problem 6

Philip is twice as old as Ben. If 5 is subtracted from Philip’s age and 10 is added to Ben’s age, then their ages will be equal. How old are both of them?

Scratch Work

Ben is x years old and Philip is 2x. If we subtract 5 from Philip’s age, it will become 2x - 5. If we add 10 to Ben’s age, it will be x + 10. Now, after the results to these operations, their ages will be equal or

2x - 5 = x + 10

Solution

Let x be Ben’s age and 2x be Philip’s age.

2x - 5 = x + 10

2x - x = 10 + 5

x = 15.

So, Ben is 15 and Philip is 30.

Check

Philip is 30 and Ben is 15 so, Philip is twice as old Ben. Subtracting 10 from Philip’s age results to 20. Adding 5 to Ben’s age is 20. Well, 20 equals 20, so we are correct.

In the next post, we will be discussing more age problems. Please keep posted.

Related Posts Plugin for WordPress, Blogger...

You may also like...

2 Responses

  1. Nobody says:

    I noticed that there is a discrepancy between the given numbers of subtracted from and added to in Problem #6 and its checking part. I was left confused, thats all. Thanks

  1. March 27, 2014

    […] How to Solve Age Problems Part 2┬ádiscusses a slightly more difficult 2-person problems particularly present-past and present-future age relationships. […]

Leave a Reply

Your email address will not be published. Required fields are marked *