In a bag, Bag C, the ratio of red counters to yellow counters is 3 : 4.
If 3 of the red counters are removed from Bag C, the ratio of red counters
to yellow counters is 3 : 5.

How many yellow counters are in Bag C?

Let the number of red counters and yellow counters in Bag C initially be \( 3x \) and \( 4x \), respectively, where \( x \) is a positive integer.

### Step 1: Before the removal of red counters
- The initial ratio of red to yellow counters is given as \( 3:4 \), so:
\[
\text{Red counters} = 3x
\]
\[
\text{Yellow counters} = 4x
\]

### Step 2: After removing 3 red counters
- When 3 red counters are removed, the number of red counters becomes \( 3x - 3 \).
- The new ratio of red to yellow counters is now \( 3:5 \), so:
\[
\frac{3x - 3}{4x} = \frac{3}{5}
\]

### Step 3: Solve the equation
We can now solve the equation for \( x \):

\[
\frac{3x - 3}{4x} = \frac{3}{5}
\]

Cross-multiply to get rid of the fractions:

\[
5(3x - 3) = 3(4x)
\]

This simplifies to:

\[
15x - 15 = 12x
\]

Now, solve for \( x \):

\[
15x - 12x = 15
\]
\[
3x = 15
\]
\[
x = 5
\]

### Step 4: Calculate the number of yellow counters
Since the number of yellow counters is \( 4x \), substitute \( x = 5 \):

\[
\text{Yellow counters} = 4 \times 5 = 20
\]

Thus, there are **20 yellow counters** in Bag C.

Would you like any additional explanation, or do you have any questions about this solution?

Here are some related questions:
1. What would the total number of counters be in Bag C before removing any red counters?
2. How would the problem change if more than 3 red counters were removed?
3. Can you create a similar problem with different ratios?
4. How can you determine the total number of red counters after the removal?
5. What is the effect of changing the ratio to a higher or lower fraction?

**Tip**: When solving ratio problems, setting up proportions and using cross-multiplication is an efficient way to eliminate fractions and solve for unknowns.

In a bag, Bag C, the ratio of red counters to yellow counters is 3 : 4. If 3 of the red counters are removed from Bag C, the ratio of red counters to yellow counters is 3 : 5. How many yellow counters are in Bag C?

Learn how to solve a ratio problem where the initial ratio of red to yellow counters is 3:4 in Bag C, and changes after removing 3 red counters. This problem covers key concepts like setting up ratios, using algebra to solve proportions, and cross-multiplication. Suitable for Grades 6-8.

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