LINEAR EQUATIONS

Activity 2: Guess My Age Puzzles

Here, we will make puzzles that we help us find people’s age.

Suppose there are four friends, three of them are 12 years old, and one is 14. Since we know the ages of all four friends, let us bring together this information. Thus, 3 people are 12 years old, and 1 person is 14 years old.
Now, let us write the age of the older person in terms of the ages of the other 3 people. We can write, 14 = 12 + 2.
And, sum of the ages of all the four friends = 12 + 12 + 12 +14 = 36 +14 = 50 years.

We will now use a tool which will help us to find out this kind of information. Let us first see how in the GIF below:

Select the ages of the four people through the given boxes and click on the “Calculate” button.
You can see how the different values are shown below the calculate button. If you want to erase the board, click on the “Erase” button.

Replay Animation

We will now try to use the tool to form a few puzzles.
 

Puzzle 1: The sum of the ages of 4 friends is 50 years. Three of the friends are of the same age, the fourth friend is older than the others by 2 years. What is the age of each friend?

We will see how we can arrive at the answer with the help of equations:
 

Let the age of the three friends be x years.

So, the sum of their ages would be x + x + x = 3x.

The age of the older friend would then be x + 2 years.
 

Since we know that the sum of the ages of the four friends is 50 years. So, we can write the equation as:

3x + (x+2) = 50

or, 4x + 2 = 50

or, 4x = 50 − 2

or, 4x = 48

or, x = 12 years, which is the age of three of the four friends.
Now, we can calculate the age of their older friend, which is x+2 = 12+2 = 14 years.

Puzzle 2: There are four friends. One of them is 14 years old. The other three friends are of the same age. The sum of all their ages is 50 years. Find the age of the three friends.

Here, the equations are slightly different from the ones in the earlier puzzle.

Let the ages of the three friends be x. 
Then, the sum of their ages  is x + x + x= 3x.
The sum of the ages of the four friends is 50 years. So,

3x + 14 = 50

or, 3x = 36

or, x =12.
Thus,  the age of the three younger friends is 12 years.

Let us now solve some more puzzles on age.

Question 1: In a group of four people, the youngest is 5 years old and the oldest is 10 years older than the youngest. The other two are of the same age, and the sum of their ages is 30 years. Find the age of each person in the group.

Task: Using the Age Tool Puzzle-Maker, create puzzles based on age. But first, solve them yourself and then post these puzzles in the Comment box (below).

You can check the answers posted by your friends. Then, invite your friends to post puzzles of their own. You can post your answers by clicking on the Reply button below the comments. You will also be able to check if your friends have posted their answers to the puzzles you set.