Kira had a roll of blue paper and a roll of red paper. The length of the roll of blue paper is 1/2 the length of the roll of red paper. She cut the roll of blue paper into equal parts of length 9 cm and on each part she drew 3 star shapes. After that, she cut the roll of red paper into equal parts of length 7 cm and on each part she drew 5 heart shapes. What fraction of the shapes Kira drew were star shapes?

Question

Kira had a roll of blue paper and a roll of red paper. The length of the roll of blue paper is 1/2 the length of the roll of red paper. She cut the roll of blue paper into equal parts of length 9 cm and on each part she drew 3 star shapes. After that, she cut the roll of red paper into equal parts of length 7 cm and on each part she drew 5 heart shapes. What fraction of the shapes Kira drew were star shapes?

Answer 1

Let the length of the blue paper roll be B cm.

Then, the length of the red paper roll is 2B cm.
The number of equal parts of length 9 cm that Kira cuts the blue paper into is B/9.
So, the number of star shapes she draws is 3*(B/9) = B/3.
The number of equal parts of length 7 cm that Kira cuts the red paper into is (2B)/7 = 2B/7.
So, the number of heart shapes she draws is 5*(2B/7) = 10B/7.
Thus, the fraction of shapes Kira drew that were star shapes is (B/3)/(B/3 + 10B/7).
This simplifies to (B/3)/(7B/21 + 30B/21) = (B/3)/(37B/21) = B/3 * 21/37B = 21/3*37 = <<21/3*37=7/37>>7/37.
Therefore, the fraction of shapes Kira drew that were star shapes is 7/37. Answer: \boxed{\frac{7}{37}}.

Answer 2

Let's break down the problem step by step.

Step 1: Determine the length of the blue paper roll relative to the red paper roll.
Given that the length of the blue paper roll is 1/2 the length of the red paper roll, we can represent this as a fraction: length of blue roll/length of red roll = 1/2.

Step 2: Calculate the number of blue paper parts.
Since Kira cut the blue paper into equal parts of length 9 cm, we need to determine how many parts she obtained. To do this, we divide the length of the blue roll by the length of each part: number of blue parts = (length of blue roll)/(length of each part).

Step 3: Calculate the number of star shapes on the blue paper.
Since Kira drew 3 star shapes on each part, the total number of star shapes on the blue paper would be: number of star shapes on blue paper = number of blue parts * 3.

Step 4: Calculate the number of red paper parts.
Using a similar approach to step 2, we divide the length of the red paper roll by the length of each part to calculate the number of red parts: number of red parts = (length of red roll)/(length of each part).

Step 5: Calculate the number of heart shapes on the red paper.
As Kira drew 5 heart shapes on each red part, the total number of heart shapes on the red paper is: number of heart shapes on red paper = number of red parts * 5.

Step 6: Calculate the fraction of shapes that are star shapes.
Finally, we need to determine the fraction of shapes that are star shapes in relation to the total number of shapes. To do this, we divide the number of star shapes on the blue paper by the sum of the number of star shapes on the blue paper and the number of heart shapes on the red paper: fraction of star shapes = (number of star shapes on blue paper) / (number of star shapes on blue paper + number of heart shapes on red paper).

By following these steps, we can find the fraction of shapes that Kira drew as star shapes.