during an art contest at your school, you and a classmate each won blue ribbons for one-third of the pieces you entered in the contest. You won 2 blue ribbons and your classmate won 3 blue ribbons. Explain how this could be

You must have entered 6 pieces and your classmate must have entered 9 pieces.

1/3 * 6 = 2
1/3 * 9 = 3

you must have entered 6 pieces and your classmate must have entered 9 pieces.

In order to explain how this could be, let's break down the information given.

According to the problem, you and your classmate each won blue ribbons for one-third of the pieces you entered in the contest. This means that the ratio of blue ribbons you won to the number of pieces you entered is 1/3. Similarly, the ratio for your classmate is also 1/3.

Now, we are given that you won 2 blue ribbons. Since the ratio of blue ribbons to pieces entered is 1/3, we can set up the following equation:

(Blue Ribbons) / (Pieces Entered) = 1/3

Plugging in your values, we get:

2 / (Pieces Entered) = 1/3

To solve for (Pieces Entered), we can cross-multiply:

2 * 3 = 1 * (Pieces Entered)
6 = Pieces Entered

Therefore, you entered a total of 6 pieces in the art contest.

Similarly, your classmate won 3 blue ribbons. We can set up the same equation:

3 / (Pieces Entered) = 1/3

Plugging in their values, we get:

3 / (Pieces Entered) = 1/3

Cross-multiplying, we have:

3 * 3 = 1 * (Pieces Entered)
9 = Pieces Entered

Therefore, your classmate entered a total of 9 pieces in the art contest.

In summary, you won 2 blue ribbons out of 6 pieces entered, while your classmate won 3 blue ribbons out of 9 pieces entered. Both of you adhered to the condition that you would win one-third of the pieces you entered, leading to this outcome.