Answer
There are 20 black marbles in the bag.
There are 30 red marbles in the bag.
Explanation
The bag contains 50 red and black marbles.
Let the number of red marbles be x
Let the number of black marbles be y
x + y = 50
Then, for every 3 red marbles, there are 2 black marbles
3 red marbles = 2 black marbles
x red marbles = y black marbles
We can write a mathematical relationship by cross multiplying
3 × y = 2 × x
3y = 2x
2x = 3y
Divide both sides by 2
(2x/2) = (3y/2)
x = 1.5y
We can now write the two equations together
x + y = 50
x = 1.5y
We can substitute for x in the first equation
x + y = 50
x = 1.5y
1.5y + y = 50
2.5y = 50
Divide both sides by 2.5
(2.5y/2.5) = (50/2.5)
y = 20 black marbles.
x + y = 50
x = 50 - y = 50 - 20 = 30 red marbles.
Hope this Helps!!!
