There were 2/5 as many red marbles as blue marbles in a box. After 44 blue marbles were removed from the box, there were 1 1/2 times as many red marbles as blue marbles. Find the number of red marbles in the box.
B=Blue marbles, R=Red marbles
R =2/5 B
B - 44
R =1.5 * [B - 44]
2/5 B =1.5 * [B - 44], solve for B
B= 60 - Blue marbles
2/5 * 60 = 24 - Red marbles in the box.
+13 Let the number of blue marbles is B and the number of red marbles initially is R.
There were 2/5 as many red marbles as blue marbles in a box.
This gives us the equation
R=(2/5)B ------(1)
After 44 blue marbles were removed from the box, there were 3/2 times as many red marbles as blue marbles. After removing 44 blue marbles, the new number of blue marbles in the box is B−44.
At this point, the number of red marbles is R(since it remains unchanged).
The second statement gives us the equation
R=(3/2)(B−44)B ------(1)
Now from the equation (1) and (2) we have,
2/5B = 3/2(B - 44)
=> 4B = 15(B - 44)
=> 11B = 15 * 44
=> B = 60.
So, there were initially 60 blue marbles in the box.
To find the number of red marbles, we can use the first equation:
R = (2/5)B = 2/5 * 60 = 24.
The number of red marbles is 24.
