Problem Solving: Finding The Unknown Value

We are going to continue with the problem-solving skills that you will need in your GCSE math questions.

Example 1

Four brothers John, Paul, George and Ringo have their 12th, 14th, 15th and 15th birthdays today.

How many years will it be before their combined age will reach 100?

We can assume that there is a fixed additional number of years that will be added to all of their respective ages when the total adds to 100.

We can, therefore, say that John will be 12 + ‘n’ years of age, Paul will be 14 + ‘n’ years of age and the twins George and Ringo will be 15 + ‘n’ years of age. If we add all theses years together we get an expression.

Hence, their total age when the combined ages reach 100 can be expressed as:  

We can now put this in an equation and solve  for the unknown value ‘n’.

So 56+4n=100 and then 4n=44, therefore n=11

Example 2

The question states that there are 6 more girls than boys in Miss Spellings class of 24 pupils.

What is the ratio of girls to boys in this class?

Let’s suppose that we call the number of boy’s ‘x’ as we don’t know their exact number.

The question also tells us that there are 6 more girls than boys, in other words, ‘x’ plus 6 girls.

We can then say that the total number of pupils is the total number of boys plus the total number of girls.

In this case, 2x plus 6 ( x (boys) + x + 6 (girls) )

However, we already know the total number of pupils is 24 as this is what was stated in the question.

As a result, we can set up the equation 

And we can then rearrange this equation to get ‘x’ is equal to 9. Since ‘x’ was originally the number of boys, and ‘x’ plus 6 was the number of girls, it is now clear that the number of boys is 9 and the number of girls is 15.

So 2x plus 6 =24 and then 2x=18, therefore x=9

The ratio of girls to boys, in this case, is, therefore, 15:9 or simplified 5:3