Answer :
Answer: Let's say that there are a total of x counters in the bag. Then, the ratio of blue counters to red counters is 2:1, so there are 2y blue counters and y red counters for some value of y.
The ratio of small counters to large counters is 1:2, so let's say there are z small counters and 2z large counters.
We know that the rest of the blue counters that are not large are small, and that the ratio of large blue counters to small blue counters is 3:1. So, we can set up the equation:
2z - k = 3k
where k is the number of small blue counters. Solving for k, we get:
k = z/5
So, the number of large blue counters is:
2z - k = 9z/5
The fraction of counters that are red and small is given by:
y/z
Substituting the values we have found, we get:
y/z = (1/3)(2y/x)/(1/5)((2/5)x/(2/3)) = 10/27
Therefore, the fraction of counters that are red and small is 10/27.
Step-by-step explanation:
Final answer:
The fraction of counters that are red and small is 1/9, considering the given ratios of blue to red counters and small to large counters.
Explanation:
To find the fraction of the counters that are red and small, let us first understand the given ratios and apply them to our calculation.
We know that the ratio of blue counters to red counters is 2:1. So for every 3 counters (2 blue + 1 red), 1 is red.
Next, we are told that the ratio of small counters to large counters is 1:2. As it does not specify a color, this ratio applies to both red and blue counters. Therefore, only one-third of all counters are small.
It's important to note that the ratio of large blue counters to small blue counters is not immediately relevant since we're looking for small red counters.
So considering the first two ratios, we can say that the fraction of the count that are small and red is (1/3) * (1/3) = 1/9.
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