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

Algebra ->  Percentage-and-ratio-word-problems -> 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      Log On


   

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) About Me  (Show Source):
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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) About Me  (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:

%28x%2F3%29%2F%28%28x%2F3%29%2B%2810x%2F7%29%29

Multiply numerator and denominator by 3*7 = 21:

%287x%29%2F%287x%2B30x%29=%287x%29%2F%2837x%29=7%2F37

ANSWER: 7/37

Answer by MathTherapy(10555) About Me  (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 B%2F9 blue parts.
Since he drew 3 stars on each part, he drew matrix%281%2C3%2C+%28B%2F9%293%2C+%22=%22%2C+B%2F3%29 stars
Likewise, cutting the red roll into 7-cm equal lengths means that there were 2B%2F7 red parts.
Since he drew 5 hearts on each red part, he drew matrix%281%2C3%2C+%282B%2F7%295%2C+%22=%22%2C+10B%2F7%29 hearts 
Total shapes (stars and hearts) drawn: 
Fraction of total shapes drawn that were stars: