Question

ii - constructed response
write each ratio as a fraction in simplest form.

1. 27:9
2. 24 to 60

the high school soccer team won seven games and lost 13 games.
a. write the ratio of wins to losses.
b. write the ratio of losses to total games played.
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: Analyze the ratio - meaning

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

Step2: Set up proportion

Let $x$ be the number of orange marbles. We know the ratio of orange to black is 5:12, and there are 72 black marbles. So we set up the proportion $\frac{x}{72}=\frac{5}{12}$.

Step3: Cross - multiply and solve

Cross - multiplying gives us $12x = 5\times72$. Since $5\times72 = 360$, then $12x=360$. Dividing both sides by 12, we get $x = 30$.

Answer:

a. For every 5 orange marbles, there are 12 black marbles.
b. 30