Question

In a bag, the ratio of white counters to pink counters was 2: 3.

6 more white counters were then added to the bag, and the ratio of white counters to pink counters became 4: 3
How many pink counters are in the bag?

Answer 1

By expressing the original ratio of white to pink counters as 2x to 3x and solving the equation derived after adding 6 white counters, we find that there are 9 pink counters in the bag.

Step-by-step explanation:

The student has provided us with a problem involving ratios and counters. Initially, the ratio of white counters to pink counters in a bag was 2:3. Upon adding 6 more white counters, the ratio changed to 4:3.

Let's denote the original number of white counters as 2x and the number of pink counters as 3x based on the initial ratio of 2:3. After adding 6 white counters, the number of white counters becomes (2x + 6).

To find the new ratio, we set up the equation (2x + 6) / 3x = 4 / 3. This can be solved in the following steps:

1. Cross multiply to get: 3(2x + 6) = 4(3x)
2. Distribute and simplify the equation: 6x + 18 = 12x
3. Subtract 6x from both sides: 18 = 6x
4. Divide both sides by 6 to find the value of x: x = 3

Solving for x gives us the multiple we need to apply to the original ratio to find the number of pink counters. As per the original ratio, we multiply x by 3 to get the number of pink counters: 3 * 3 = 9

Therefore, there are 9 pink counters in the bag.