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.
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To explain how this could be, we need to consider the number of pieces of art both you and your classmate entered. Since you won 2 blue ribbons, and that represents 1/3 of the pieces you entered, we can multiply 2 by 3 to find the total number of pieces you entered. This gives us 6.
Similarly, your classmate won 3 blue ribbons, which also represents 1/3 of the pieces they entered. We can multiply 3 by 3 to find the total number of pieces your classmate entered. This also gives us 9.
Therefore, you and your classmate entered a total of 6 + 9 = 15 pieces of art.
To understand how this could be possible, let's break down the given information step by step.
We know that you and your classmate won blue ribbons for only 1/3 of the pieces you entered in the contest. This means that out of the total number of art pieces entered, only 1/3 received blue ribbons.
Next, we're told that you won 2 blue ribbons and your classmate won 3 blue ribbons. This implies that the total number of blue ribbons awarded to both of you is 2 + 3 = 5.
Now, assuming that each blue ribbon represents 1/3 of the art pieces, we can set up an equation to determine the total number of art pieces entered.
Let x be the total number of art pieces entered.
Since 1/3 of the art pieces received blue ribbons, we can calculate this as x * 1/3.
Given that the total number of blue ribbons won by you and your classmate is 5, we can set up another equation:
2 + 3 = 5 = x * 1/3.
To solve for x, we can multiply both sides of the equation by 3 to get rid of the fraction:
3 * 5 = x * 1.
This simplifies to:
15 = x.
So, the total number of art pieces entered in the contest is 15.
To summarize, it is possible for you and your classmate to each win blue ribbons for only 1/3 of the pieces you entered in the contest if you entered a total of 15 art pieces.