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.