during an art contest at your school,you and a classmate each won blue ribbons for 1/3 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 because 1/3 of 6 = 2.

How many pieces did your classmate enter?

nine

To understand how this could be, let's break it down step-by-step:

1. It is mentioned that you and your classmate each won blue ribbons for 1/3 of the pieces you entered in the contest. This means that for every 3 pieces each of you entered, you each won a blue ribbon.

2. It is further stated that you won 2 blue ribbons and your classmate won 3 blue ribbons. This means that you entered a total of 3 * 2 = 6 pieces in the contest.

3. Using this information, we can calculate the number of pieces your classmate entered. If you entered 6 pieces in total and won 2 blue ribbons, then your classmate must have entered 6 - 2 = 4 pieces in total.

4. Now let's calculate the number of blue ribbons earned by you and your classmate. Since each of you won a blue ribbon for every 3 pieces entered, you won 2 ribbons out of your 6 pieces, which is a ratio of 2/6. Similarly, your classmate won 3 ribbons out of their 4 pieces, which is a ratio of 3/4.

5. In order to compare the two ratios, we can convert them to a common denominator. The least common multiple of 6 and 4 is 12. Multiplying the first ratio (2/6) by 2/2 and the second ratio (3/4) by 3/3, we get 4/12 and 9/12 respectively.

6. Comparing the two ratios, we can see that you won 4 out of 12 blue ribbons, and your classmate won 9 out of 12 blue ribbons. This means that you won 1/3 of the blue ribbons (4/12) and your classmate won 2/3 of the blue ribbons (9/12).

Therefore, based on the given information, it is possible for you to have won 2 blue ribbons and your classmate to have won 3 blue ribbons in an art contest where you both entered 1/3 of the pieces and won blue ribbons accordingly.