I have no idea, but I guessed 5 pieces won out of 15. Anyhow here is the question.
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.
1/3 of what # is 2. That must be 6. So you entered 6 pieces.
1/3 of what # is 3. Tht must be 9. So your friend entered 9 pieces.
Total pieces is 9 + 6 = 15.
You did well for guessing. Your intuition is working well today.
Based on your description and the information provided, it seems that you and your classmate each won blue ribbons for 1/3 of the pieces you entered in the art contest. You won 2 blue ribbons, and your classmate won 3 blue ribbons. To explain how this could be, let's break it down step by step:
First, let's determine the total number of blue ribbons that were awarded. Since you won 2 blue ribbons and your classmate won 3 blue ribbons, the total number of blue ribbons awarded is 2 + 3 = 5.
Next, we need to find out the fraction of the total pieces that each of you entered. According to the information given, each of you won blue ribbons for 1/3 of the pieces entered.
To figure out the total number of pieces you entered, we need to find the whole number that 1/3 of it equals 2 (the number of blue ribbons you won). We can solve this by multiplying 2 by the reciprocal of 1/3:
2 * 3/1 = 6.
So, you entered a total of 6 pieces in the art contest.
Similarly, we can find out the total number of pieces your classmate entered. We know that 1/3 of some number equals 3 (the number of blue ribbons your classmate won). Again, we can solve this by multiplying 3 by the reciprocal of 1/3:
3 * 3/1 = 9.
Therefore, your classmate entered a total of 9 pieces in the contest.
To verify the total number of pieces entered, we add up the pieces entered by you and your classmate: 6 + 9 = 15.
So, in total, there were 15 pieces entered in the art contest.
In summary, you and your classmate won blue ribbons for 1/3 of the pieces you each entered. You won 2 blue ribbons, which means you entered 6 pieces, and your classmate won 3 blue ribbons, which means they entered 9 pieces. The total number of pieces entered in the contest was 15.