Number problems - percentages and fractions
Example 2
Mrs Brown has two jars of sweets. The jars contain the same number of sweets in total.
- 25% of the sweets in Jar A are mint.
- Two fifths of the sweets in Jar B are mint.
There are 10 mint sweets in Jar A, how many mint sweets are there in Jar B?
1. What do I have to do?
Read the question through twice. Highlight or underline the important pieces of information in the question.
2. What information do I need?
The most important parts of this question are 25% of the sweets in Jar A are mint and two fifths of Jar B are mint. It is clear this question is going to involve using fractions and percentages.
The question asks how many mints are in jar B. The answer needs to be a number rather than a percentage or fraction.
Two fifths is equivalent to \(\frac{4}{10}\) = 40%, which is greater than 25% so there are more sweets in Jar B.
3. What information don’t I need?
Everything in this question is relevant to working out the answer.
4. What maths can I do?
The most important parts of this question are 25% of the sweets in Jar A are mint and two fifths of those in Jar B are mint. This provides the way into the question.
Step A
Look at the information given.
There are 10 mint sweets in Jar A.
25% of the sweets in Jar A are mint ones.
Therefore 25% of Jar A must be 10 mint sweets.
Step B
Now find the number of sweets in Jar A.
The total number of sweets in Jar A is 100%.
If 25% is 10 sweets, 100% is four times 25% therefore there must be \(10 \times 4 = 40\) sweets in Jar A.
Step C
Now find the number of mint sweets in Jar B.
There is the same number of sweets in each jar.
Therefore Jar B must also contain 40 sweets.
Two fifths of Jar B are mint sweets therefore \(\frac{2}{5}\) of 40 needs to be found.
Firstly find \(\frac{1}{5}\) of 40 by dividing by 5.
\(40 \div 5 = 8\)
Now find two fifths by multiplying your answer by 2.
\(8 \times 2 = 16\)
There are therefore 16 mint sweets in Jar B.
5. Is my solution correct?
It is important to check any calculations at the end, even if a calculator was used.
There should be more mint sweets in Jar B than Jar A, which there is.
6. Have I completed everything?
The answer is supposed to be a whole number of sweets, which it is.
Nothing else was asked for.
