# A bag contains 100 marbles, some contains red, the rest blue. If there are no more than 1 times as many red marbles as blue ones in the bag, at most how many red marbles are in the bag? At least how many blue ones are in the bag?

Nov 23, 2017

The maximum number of red marbles is 50.
The minimum number of blue marbles is 50.

#### Explanation:

Let red marbles be $r$ and blue marbles be $b$.

If there are no more than 1 times as many red marbles as blue ones, an inequality can be formed,

$r \le b$

We can use substitution to find the maximum number of red marbles and minimum number of blue marbles,

$r + b = 100$
$b = 100 - r$

Substitute $b = 100 - r$ into $r \le b$,

$r \le 100 - r$
$2 r \le 100$
$r \le 50$

Hence, the maximum number of red marbles is 50.

To find the minimum number of blue marbles, subtract the maximum number of red marbles from 100,

$b \ge 100 - 50$
$b \ge 50$

Hence, the minimum number of blue marbles is 50.