A bag contains only red and blue counters. There are 6 more red counters than blue counters. A counter is chosen at random, and the probability of picking a blue counter is [tex]\frac{1}{4}[/tex]. How many red counters are there?

To find the number of red counters, set up an equation using the probability and the number of red and blue counters, then solve for x. The number of red counters is x + 6.

Explanation:

Let's assume that the number of blue counters is x. According to the given information, the number of red counters is 6 more than the number of blue counters, so the number of red counters is x + 6.

The total number of counters in the bag is the sum of the number of red and blue counters, which is x + (x + 6) = 2x + 6.

The probability of choosing a red counter at random is given as 1/4. Since there are x + 6 red counters in total, the probability of choosing a red counter is (x + 6) / (2x + 6) = 1/4.

Solving this equation, we can find the value of x, which represents the number of blue counters in the bag. Then we can calculate the number of red counters (x + 6) using the value of x.

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