During an art context 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
your friend entered more pieces.
In fact, you entered 6 and the classmate entered 9
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To understand how this could be possible, we should first figure out the total number of pieces that you and your classmate entered in the contest.
Let's say you and your classmate entered n pieces each. Since the both of you won 1/3 of the pieces you entered, it means that 1/3 of n pieces were awarded blue ribbons to both of you.
According to the information given, you won 2 blue ribbons, which means 2/n of the pieces you entered won the blue ribbon. Similarly, your classmate won 3 blue ribbons, indicating that 3/n of their entries won the blue ribbon.
Since the total number of blue ribbons won by both of you is the same, we can set up an equation:
2/n = 3/n
To solve this equation, we can cross-multiply:
2n = 3n
Subtracting 2n from both sides:
2n - 2n = 3n - 2n
0 = n
This tells us that the total number of pieces entered by you and your classmate is zero.
Therefore, it seems that something is incorrect or missing in the given information. Perhaps there was a miscommunication or mistake in the context of the art contest. It is advisable to gather more accurate information to explain how you and your classmate each won blue ribbons for the pieces you entered.