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

Answer:

There are 15 purple marbles.

Step-by-step 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 $x$:

$Purple\ marbles =2x-9$

$Purple\ marbles =2\times 12-9$

$Purple\ marbles =24-9$

$Purple\ marbles =15.$

Therefore, there are 15 purple marbles.