There are y yellow marbles and b blue marbles in a box. 18% of the yellow marbles were added to 24% of the blue marbles, and the total was 30. Three times the number of yellow marbles exceeds two times the number of blue marbles by 200. What is the ratio of y to b?

Question

Accepted Answer

Let y be the number of yellow marbles and b be the number of blue marbles.

Given:
18% of y + 24% of b = 30
=> 0.18y + 0.24b = 30

Also, three times the number of yellow marbles exceeds two times the number of blue marbles by 200:
3y - 2b = 200

From the first equation:
0.18y + 0.24b = 30
Multiply both sides by 100 to clear decimals:
18y + 24b = 3000
Divide entire equation by 6:
3y + 4b = 500  ...(1)

From the second equation:
3y - 2b = 200  ...(2)

Now, solve equations (1) and (2):

Add (1) and (2):
(3y + 4b) + (3y - 2b) = 500 + 200
6y + 2b = 700

From this, express b:
2b = 700 - 6y
b = (700 - 6y)/2

Substitute b into equation (2):
3y - 2 * ((700 - 6y)/2) = 200
3y - (700 - 6y) = 200
3y - 700 + 6y = 200
9y = 900
y = 100

Substitute y = 100 into equation (2):
3*100 - 2b = 200
300 - 2b = 200
-2b = 200 - 300 = -100
2b = 100
b = 50

Therefore, y = 100 and b = 50

Ratio y : b = 100 : 50 = 2 : 1

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