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 of pens that are blue.
Question
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 of pens that are blue.
Solution
Step 1: Understand the ratios
The ratio of red pens to blue pens is 5 : 9. This means for every 5 red pens, there are 9 blue pens.
The ratio of blue pens to green pens is 1 : 4. This means for every 1 blue pen, there are 4 green pens.
Step 2: Find a common multiplier
To combine these ratios, we need to find a common multiplier for the number of blue pens. In this case, it's 9 (from the first ratio) and 1 (from the second ratio). The common multiplier is 9.
Step 3: Adjust the ratios
We adjust the second ratio by multiplying both sides by 9. So, the ratio of blue pens to green pens becomes 9 : 36.
Step 4: Combine the ratios
Now, we can combine the ratios. The ratio of red pens to blue pens to green pens is 5 : 9 : 36.
Step 5: Calculate the percentage
The total number of pens is 5 (red) + 9 (blue) + 36 (green) = 50 pens.
The percentage of pens that are blue is (9/50) * 100 = 18%.
So, 18% of the pens are blue.
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