# There are 30 red and blue balls are in a box. How many balls are blue?At a random drawing out, the ball extracted has the 7/15 probability to be red.

cburr | Certified Educator

The key to solving this problem quickly is to note the connection between 30 and 15 (30 = 15 times 2).  But, even if you don't see that, you can figure it out with basic fraction math.

The problem tells you that if you pull out 15 balls, 7 of them will be red.  But we have 30 balls, not 15.  How many of the whole thing are red?

7         ?

__  =   __

15       30

In the denominator you have to multiply 15 by 2 to get to 30, so do the same in the numerator -- 7 times 2 is 14.

7 x 2     14

__    =   __

15 x 2    30

Remember, this is how many are red. Now we have to find out how many are blue.

30 - 14 = 16

So, the answer is that 16 balls are blue.

mcetner | Certified Educator

Since you know the probability of drawing a red ball is 7/15, and you know the amount of balls in the box is 30, then you can make a proportion:

probability 7/15 = x/30.  Solve for x by cross-multiplying and get x = 14.  This means out of 30 balls, 14 are red.

Now, since the only other choice is blue, just subtract and 30 - 14 = 16 blue balls in the box.

atyourservice | Student

There are 30 red and blue balls are in a box. How many balls are blue?

At a random drawing out, the ball extracted has the 7/15 probability to be red

if 7/15 are red it means that 8/15 are red, so the first step is to set up a proportion:

`8/15 = x/30`

cross multiply:

15x = 240

divide by 15:

`(15x)/15 = (240)/15`

x = 16

16 of the balls are blue

revolution | Student

7/15=x/30 (propability)

15x=7*30

15x=210

x=14 (red)

blue balls= 30-14=16