A box contains only red, blue and green pens - OCR - GCSE Maths - Question 2 - 2018 - Paper 1
Question 2
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 2 - 2018 - Paper 1
Step 1
Step 1: Determine the common ratios
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Answer
To solve the problem, we first need to find a common term for the blue pens. From the given ratios, we have:
Red to Blue = 5 : 9
Blue to Green = 1 : 4
Let’s express the number of blue pens in terms of the other colors. To align the ratios, let’s rewrite the second ratio by multiplying both sides by 9 (since the blue pen's factor is 9 in the first ratio):
Blue = 9
Green = 9 * 4 = 36
Now we can express the red pens in terms of blue pens:
Red = (5 / 9) * 9 = 5
Thus, the complete ratio of Red : Blue : Green is 5 : 9 : 36.
Step 2
Step 2: Calculate total number of pens
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Answer
Now that we have the amounts of each color of pen, we can calculate the total number of pens:
Total Pens = Red + Blue + Green = 5 + 9 + 36 = 50.
Step 3
Step 3: Calculate the percentage of blue pens
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Answer
Finally, we calculate the percentage of pens that are blue:
Percentage of Blue Pens = (Number of Blue Pens / Total Number of Pens) * 100
