Question

at the roslindale library, there are 6 books with white main characters for every 4 books with a bipoc main character.
a. does that mean there are only 10 books at the library? explain why or why not.
b. if there are 12 books with white main characters, how many are there with bipoc main characters? show your work.
c. if there are 24 books with white main characters, how many are there with bipoc main characters? show your work.
d. if there are 20 books with bipoc main characters, how many are there with white main characters? show your work.

Explanation:

Step1: Analyze the ratio

The ratio of books with White main characters to books with BIPOC main characters is \(6:4 = 3:2\). This is a proportion, not the actual number of books. So, there could be multiples of this ratio (e.g., \(12:8\), \(18:12\) etc.).

Step2: Solve part b

Let \(x\) be the number of BIPOC - character books. Set up the proportion \(\frac{6}{4}=\frac{12}{x}\). Cross - multiply: \(6x = 4\times12\), \(6x=48\), \(x = 8\).

Step3: Solve part c

Let \(y\) be the number of BIPOC - character books. Set up the proportion \(\frac{6}{4}=\frac{24}{y}\). Cross - multiply: \(6y = 4\times24\), \(6y = 96\), \(y = 16\).

Step4: Solve part d

Let \(z\) be the number of White - character books. Set up the proportion \(\frac{6}{4}=\frac{z}{20}\). Cross - multiply: \(4z=6\times20\), \(4z = 120\), \(z = 30\).

Answer:

a. No. The ratio \(6:4\) is a proportion. The actual number of books is a multiple of \(6 + 4=10\) (e.g., \(10\), \(20\), \(30\) etc.).
b. \(8\)
c. \(16\)
d. \(30\)