Question 1202919
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.