SOLUTION: 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 pa

Question 1202919: 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?
Found 3 solutions by Theo, greenestamps, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let the length of the blue roll equal x.
then the length of the red roll equals 2x.
the number of stars in the blue roll = s = x/9 * 3 = x/3
the number of hearts in the red roll = h = 2x/7 * 5 = 10x/7
you get s = x/3 and h = 10x/7
solve for x in both equations to get:
x = 3s
x = 7h/10
since they both equal to x, you can set them equal to each other to get:
3s = 7h/10
solve for s to get s = 7h/30
the ratio of star to total is equal to s/(s + h)
the ratio of hearts to total is equal to h/(s + h)
since s = 7h/30, then s + h = 7h/30 + h which is equal to 7h/30 + 30h/30 which is equal to 37h/30.
s / (s+h) is equal to s / (37h/30) which is equal to (7h/30) / (37h/30) which is equal to 7h/30 * 20/37h which is equal to 7h/37h which is equal to 7/37.
h / (s+h) is equal to h / (37h/30) which is equal to h * 30/37h which is equal to 30h / 37h which is equal to 30/37.
the fraction of the star shapes to the total shapes that kira drew was 7/37.
that's your solution.

note that the x for the blue roll and 2x for the red roll had to be multiples of 63 because x had to be evenly divisible by 9 and 2x had to be evenly divisible by 7.
the least common multiple of 7 and 9 is 63.

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!

Let x = length of blue paper
Then 2x = length of red paper

number of pieces of blue paper: x/9
number of pieces of red paper: 2x/7

number of stars: 3(x/9) = x/3
number of hearts: 5(2x/7) = 10x/7

The fraction of shapes that were stars is the number of stars, divided by the total number of shapes:

Multiply numerator and denominator by 3*7 = 21:

ANSWER: 7/37

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!

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? Let length of blue paper be B Then length of red paper = 2B Cutting the blue roll into 9-cm equal lengths means that there were blue parts. Since he drew 3 stars on each part, he drew stars Likewise, cutting the red roll into 7-cm equal lengths means that there were red parts. Since he drew 5 hearts on each red part, he drew hearts Total shapes (stars and hearts) drawn: Fraction of total shapes drawn that were stars:

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