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A pencil case contains only blue, purple and pink pencils. The ratio of blue pencils to purple pencils is 14:9. The ratio of purple pencils to pink pencils is 1:3. Calculate the percentage of pencils that are pink. Submit Answer

A pencil case contains only blue, purple and pink pencils.\newline The ratio of blue pencils to purple pencils is 14:9 14: 9 . \newlineThe ratio of purple pencils to pink pencils is 1:3 1: 3 .\newlineCalculate the percentage of pencils that are pink.\newline

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Q. A pencil case contains only blue, purple and pink pencils.\newline The ratio of blue pencils to purple pencils is 14:9 14: 9 . \newlineThe ratio of purple pencils to pink pencils is 1:3 1: 3 .\newlineCalculate the percentage of pencils that are pink.\newline
  1. Define Pencil Ratios: Let's define the number of blue, purple, and pink pencils as BB, PP, and KK respectively. Given the ratio of blue to purple pencils is 14:914:9, we can write B=14xB = 14x and P=9xP = 9x for some multiplier xx.
  2. Calculate Pink Pencils: Next, the ratio of purple pencils to pink pencils is 1:31:3. So, for every purple pencil, there are 33 pink pencils. This gives us K=3PK = 3P. Substituting P=9xP = 9x from the previous step, we get K=3(9x)=27xK = 3(9x) = 27x.
  3. Find Total Pencils: Now, we need to find the total number of pencils, which is the sum of blue, purple, and pink pencils. So, Total=B+P+K=14x+9x+27x=50x\text{Total} = B + P + K = 14x + 9x + 27x = 50x.
  4. Calculate Percentage: To find the percentage of pink pencils, we calculate (Number of Pink PencilsTotal Number of Pencils)×100(\frac{\text{Number of Pink Pencils}}{\text{Total Number of Pencils}}) \times 100. Substituting the values, we get (27x50x)×100=54%(\frac{27x}{50x}) \times 100 = 54\%.

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