Question

# If Leah is 6 years older than Sue and John is 5 years older than Leah and the total of their ages is 41. Then how old is Sue?

Hint: After carefully reading the question we can see that three statements are given. Formulate three equations based on those three statements and then solve them. To get started, we will assume Sue’s age as x years. Then, we will get Leah’s age as x+6 years and similarly we can get John’s age too. After solving those equations, get the desired age.

It is given in the question that,
1. Leah is 6 years older than Sue.
2. John is 5 years older than Leah.
3. The total of their ages is 41
Now, we have to formulate equations based on the above written statements. So, let us suppose that the age of Sue is $x$ years.
Then as it is given that Leah is 6 years older than Sue, so
Leah’s age = $x+6$ years
Also, it is given that John is 5 years older than Leah, so
John’s age = $(x+6)+5=x+11$ years
Now, finally the sum of their ages is equal to 41, so
$\therefore$ Sue’s age + Leah’s age + John’s age = 41
$\Rightarrow x+(x+6)+(x+11)=41$
Simplifying the above equation, we get
$\Rightarrow 3x+17=41$
Rearranging the above equation, we get
$\Rightarrow 3x=41-17=24$
Dividing both sides by 3, we get
$\Rightarrow x=\dfrac{24}{3}=8$
Here, the value of $x$ is 8.

Hence, Sue is 8 years old.

Note: This question tests the basic understanding of Linear equations in one variable and there is no tricky part in it. Students must carefully read the question and try to find the statements given in it and then formulate equations according to the statements. Finally solve those equations and get the desired value. If students assume Leah’s age as x years, then it will give them different ages - Sue’s age as x-6 years and John’s age as x+5 years. Then after finding the value of x , students would have to substitute it in x-6 to get Sue’s age. This will increase calculation, so it is better to assume Sue’s age as x.