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A box contains only red, blue and green pens - OCR - GCSE Maths - Question 20 - 2018 - Paper 1
Question 20
A box contains only red, blue and green pens. The ratio of red pens to blue pens is 5 : 9. The ratio of blue pens to green pens is 1 : 4. Calculate the percentage o... show full transcript
Worked Solution & Example Answer:A box contains only red, blue and green pens - OCR - GCSE Maths - Question 20 - 2018 - Paper 1
Step 1
Calculate the total ratio of pens
Answer
We start with the given ratios:
- Red to Blue: 5:9
- Blue to Green: 1:4
We first express the Blue to Green ratio in terms of Blue. Let the number of Blue pens be represented as 1 unit, then:
- If Blue = 4 units (as per its ratio with Green), then the number of Green pens is 4 units.
Now to adjust the Red to Blue ratio:
- Red (for 9 Blue) = 5 units
- Thus, if we assume 9 units of Blue, we can express everything based on Blue's multiples:
- Red = 5/9 * 9 = 5 units,
- Blue = 9 units,
- Green = 4/1 * 9 = 36/4 = 9 units covering Green.
Total Ratio = Red + Blue + Green = 5 + 9 + 36 = 50.
Step 2
Calculate the percentage of blue pens
Answer
The total number of pens is 50 units, and the Blue pens total 9 units. The percentage of Blue pens is calculated as follows:
[ \text{Percentage of Blue Pens} = \left( \frac{\text{Number of Blue Pens}}{\text{Total Number of Pens}} \right) \times 100 ]
[ = \left( \frac{9}{50} \right) \times 100 = 18% ]
So, the percentage of pens that are blue is 18%.