Question

1. a container full of marbles has a ratio of orange - marbles to black marbles of 5:12. a. what does this ratio mean? b. if a container held 72 black marbles, how many orange marbles are in the container?

Explanation:

Step1: Interpret the ratio meaning

The ratio of orange marbles to black marbles is 5:12. It means for every 12 black - marbles, there are 5 orange marbles.

Step2: Set up a proportion

Let the number of orange marbles be $x$. We have the proportion $\frac{x}{72}=\frac{5}{12}$.

Step3: Cross - multiply and solve

Cross - multiplying gives $12x = 72\times5$. Then $12x=360$. Dividing both sides by 12, we get $x = 30$.

Answer:

a. It means that for every 12 black marbles, there are 5 orange marbles in the container.
b. 30