I am trying to help my son figure out this question.
during an art class at your school, you and a class mate each won blue ribbons for 1/3 of the pieces you entered in to the contest. you won 2 blue ribbons and your classmate won 3. explain how this could be
You must have entered 6 pieces. How many did your classmate enter?
To explain how this could be, let's break down the information step by step:
1. The question states that you and your classmate each won blue ribbons for 1/3 of the pieces you entered into the contest.
2. Given that you won 2 blue ribbons, we can infer that you entered a total of 6 pieces (since 2 is 1/3 of 6).
3. Similarly, since your classmate won 3 blue ribbons, we can conclude that your classmate also entered a total of 9 pieces (since 3 is 1/3 of 9).
4. Therefore, it is possible for you and your classmate to have different winning ratios. You won 2 out of 6 (or 1/3) pieces, while your classmate won 3 out of 9 (also 1/3) pieces.
In summary, you and your classmate could have different numbers of pieces entered into the contest, resulting in you winning 2 blue ribbons and your classmate winning 3 blue ribbons.
To solve this problem, we need to understand the given information.
Let's break it down step by step:
1. It is mentioned that you and your classmate won blue ribbons for 1/3 of the pieces you entered into the contest. This means that the total number of pieces entered by both of you is divisible by 3.
2. It is stated that you won 2 blue ribbons and your classmate won 3. Together, you both won a total of 5 blue ribbons.
3. Since the total number of blue ribbons won must be divisible by 3 according to the given information, let's try to find a number that satisfies this condition.
4. We can start by looking at multiples of 3 and checking if any combination of blue ribbons adds up to 5.
If we try with 3 pieces, it won't work since no combination of 2 and 3 will give us 5.
If we try with 6 pieces, we can divide them equally between you and your classmate. You would have 2 blue ribbons, and your classmate would also have 2 blue ribbons. So, in this case, the total number of blue ribbons won is 4, which does not match the given total of 5 blue ribbons.
5. Let's continue trying with higher multiples of 3. If we consider 9 pieces, we have two possibilities:
- You win 2 blue ribbons and your classmate wins 3 blue ribbons, making a total of 5 blue ribbons.
- Alternatively, you can both win 1 blue ribbon each, totaling 2 blue ribbons.
6. Therefore, the solution is that you and your classmate entered a total of 9 pieces into the contest. You won 2 blue ribbons, and your classmate won 3 blue ribbons.
So, you can explain to your son that the situation could occur if you and your classmate entered 9 pieces in the contest, and you won 2 blue ribbons while your classmate won 3.