In a bag, the ratio of red to blue counters is 3 : 4. If 3 red counters are removed the ratio of red to blue counters becomes 3 : 5. How many blue counters are there in the bag? *
r/b = 2/3, so r = 2/3 b
(r-3)/b = 3/5
5(r-3) = 3b
5(2/3 b - 3) = 3b
now finish solving for b
Let's assume the number of red counters in the bag is 3x, and the number of blue counters is 4x (according to the initial ratio of 3:4).
After removing 3 red counters, there will be 3x-3 red counters left in the bag. At this point, the ratio of red to blue counters is given as 3:5.
So, we have (3x-3)/(4x) = 3/5.
Cross-multiplying, we get 5(3x-3) = 3(4x).
Simplifying, we get 15x - 15 = 12x.
Bringing like terms to one side, we get 15x - 12x = 15.
Combining like terms, we get 3x = 15.
Dividing both sides by 3, we get x = 5.
Since the number of blue counters is 4x, the number of blue counters in the bag is 4(5) = 20.
Therefore, there are 20 blue counters in the bag.
To find the number of blue counters in the bag, we'll use a method of solving simultaneous equations.
Let's assume the initial number of red counters in the bag is 3x and the number of blue counters is 4x.
According to the problem, when 3 red counters are removed, the ratio of red to blue counters becomes 3 : 5. So, after removing 3 red counters, there are 3x - 3 red counters and 4x blue counters remaining.
We can set up the following equation based on the given information:
(3x - 3) / (4x) = 3 / 5
Now, let's solve this equation to find the value of x:
Cross multiplying, we have:
5(3x - 3) = 3(4x)
15x - 15 = 12x
Simplifying, we get:
15x - 12x = 15
3x = 15
x = 5
Now that we know the value of x is 5, we can substitute it back into our original assumption to find the number of blue counters:
Number of blue counters = 4x = 4 * 5 = 20
Therefore, there are 20 blue counters in the bag.