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how to solve using ratio

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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.

Aug 6, 2023

#1
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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.

Aug 6, 2023
#2
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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.

Aug 7, 2023