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

Define Pencil Ratios: Let's define the number of blue, purple, and pink pencils as B, P, and K respectively. Given the ratio of blue to purple pencils is 14:9, we can write B = 14x and P = 9x for some multiplier x. Calculate Pink Pencils: Next, the ratio of purple pencils to pink pencils is 1:3. So, for every purple pencil, there are 3 pink pencils. This gives us K = 3P. Substituting P = 9x from the previous step, we get K = 3(9x) = 27x. 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. Calculate Percentage: To find the percentage of pink pencils, we calculate (Number of Pink Pencils / Total Number of Pencils) * 100. Substituting the values, we get (27x / 50x) * 100 = 54%.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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 $14: 9$ . $\newline$ The ratio of purple pencils to pink pencils is $1: 3$ . $\newline$ Calculate the percentage of pencils that are pink. $\newline$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations using substitution: word problems

Full solution

Q. A pencil case contains only blue, purple and pink pencils.

\newline

The ratio of blue pencils to purple pencils is

14: 9

\newline

The ratio of purple pencils to pink pencils is

1: 3

\newline

Calculate the percentage of pencils that are pink.

\newline

Define Pencil Ratios: Let's define the number of blue, purple, and pink pencils as $B$ , $P$ , and $K$ respectively. Given the ratio of blue to purple pencils is $14:9$ , we can write $B = 14x$ and $P = 9x$ for some multiplier $x$ .
Calculate Pink Pencils: Next, the ratio of purple pencils to pink pencils is $1:3$ . So, for every purple pencil, there are $3$ pink pencils. This gives us $K = 3P$ . Substituting $P = 9x$ from the previous step, we get $K = 3(9x) = 27x$ .
Find Total Pencils: Now, we need to find the total number of pencils, which is the sum of blue, purple, and pink pencils. So, $\text{Total} = B + P + K = 14x + 9x + 27x = 50x$ .
Calculate Percentage: To find the percentage of pink pencils, we calculate $(\frac{\text{Number of Pink Pencils}}{\text{Total Number of Pencils}}) \times 100$ . Substituting the values, we get $(\frac{27x}{50x}) \times 100 = 54\%$ .