Question

A bag contains 50 marbles. Some are red and the rest are black. There are 3 red marbles for every 2 black marbles. How many black marbles are in the bag?

Answer 1

There are 20 black marbles in the bag.

There are 30 red marbles in the bag.

Step-by-step 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!!!