Question

A bag contains purple marbles and red marbles, 27 in total. The number of purple marbles is 9 less than 2 times the number of red marbles. How many purple marbles are there?

Answer 1

There are 15 purple marbles.

Explanation:

Given:

A bag contains purple marbles and red marbles, 27 in total.

The number of purple marbles is 9 less than 2 times the number of red marbles.

Now, to find the number of purple marbles.

Let the number of red marbles be
`x.`

And the number of purple marbles be
`2x-9.`

Total marbles = 27.

According to question:

`x+(2x-9)=27.`

⇒
`x+2x-9=27.`

⇒
`3x-9=27.`

Adding both sides by 9 we get:

⇒
`3x=36.`

Dividing both sides by 3 we get:

⇒
`x=12.`

So, to get the number of purple marbles we put the value of
`x`:

`Purple\ marbles =2x-9`

`Purple\ marbles =2* 12-9`

`Purple\ marbles =24-9`

`Purple\ marbles =15.`

Therefore, there are 15 purple marbles.