Question

There is a bag with only red marbles and blue marbles.

The probability of randomly choosing a red marble is
7/12
There are 84 marbles in total in the bag and each is equally likely to be chosen.
Work out how many red marbles there must be.

Answer 1

49

Explanation:

The probability of choosing a red marble is equal to the number of red marbles over the number of total marbles there are.

Therefore, let the number of red marbles be
`x`.

We have the following equation:

`(x)/(84)=(7)/(12)`

Cross-multiplying, we get:

`12x=7\cdot 84,\\x=(84\cdot 7)/(12),\\x=\boxed{49}`

Therefore, there are 49 red marbles in the bag.