Question

In a bag, the ratio of red counters to blue counters was 4/5 10 more red counters were then added to the bag, and the ratio of red counters to blue counters became 6 * 5 How many blue counters are in the bag?

Answer 1

To figure out the number of blue counters, we start from the initial ratio and solve for 'x' after establishing the new ratio. Upon finding 'x', we multiply by 5 to find that there are 25 blue counters in the bag.

Step-by-step explanation:

The student's question concerns the concept of ratio and proportion in mathematics. We are to calculate the number of blue counters in a bag given that the ratio of red counters to blue counters changes with the addition of more red counters.

Let's denote the original number of red counters as 4x and the number of blue counters as 5x based on the initial ratio of 4:5. After adding 10 more red counters, the new number of red counters becomes 4x + 10.

According to the new ratio of red to blue counters being 6:5, we can set up the proportion:

(4x + 10) / 5x = 6 / 5

Multiplying both sides by 5x gives us:

4x + 10 = 6x

Now we can solve for x:

• Subtract 4x from both sides: 10 = 2x
• Divide both sides by 2: 5 = x

Having found x, we can now calculate the number of blue counters:

5x = 5 * 5

= 25 blue counters