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Answer :
Sure! Let's solve this problem step-by-step.
1. Identify Initial Conditions:
- We know the initial ratio of white counters to pink counters is [tex]\(2:3\)[/tex].
- Let's suppose there are [tex]\(2x\)[/tex] white counters and [tex]\(3x\)[/tex] pink counters.
2. After Adding White Counters:
- 6 more white counters were added, so the new number of white counters is [tex]\(2x + 6\)[/tex].
- The ratio of white counters to pink counters becomes [tex]\(4:3\)[/tex].
3. Set Up the Equation:
- According to the new ratio, [tex]\(\frac{2x + 6}{3x} = \frac{4}{3}\)[/tex].
4. Solve the Equation:
- Cross-multiply to eliminate the fractions:
[tex]\[
3(2x + 6) = 4(3x)
\][/tex]
- Expand both sides:
[tex]\[
6x + 18 = 12x
\][/tex]
5. Simplify and Solve for [tex]\(x\)[/tex]:
- Rearrange the equation:
[tex]\[
12x - 6x = 18
\][/tex]
[tex]\[
6x = 18
\][/tex]
- Divide both sides by 6:
[tex]\[
x = 3
\][/tex]
6. Find the Number of Pink Counters:
- Since there are [tex]\(3x\)[/tex] pink counters, substitute [tex]\(x = 3\)[/tex]:
[tex]\[
3x = 3 \times 3 = 9
\][/tex]
So, there are 9 pink counters in the bag.
1. Identify Initial Conditions:
- We know the initial ratio of white counters to pink counters is [tex]\(2:3\)[/tex].
- Let's suppose there are [tex]\(2x\)[/tex] white counters and [tex]\(3x\)[/tex] pink counters.
2. After Adding White Counters:
- 6 more white counters were added, so the new number of white counters is [tex]\(2x + 6\)[/tex].
- The ratio of white counters to pink counters becomes [tex]\(4:3\)[/tex].
3. Set Up the Equation:
- According to the new ratio, [tex]\(\frac{2x + 6}{3x} = \frac{4}{3}\)[/tex].
4. Solve the Equation:
- Cross-multiply to eliminate the fractions:
[tex]\[
3(2x + 6) = 4(3x)
\][/tex]
- Expand both sides:
[tex]\[
6x + 18 = 12x
\][/tex]
5. Simplify and Solve for [tex]\(x\)[/tex]:
- Rearrange the equation:
[tex]\[
12x - 6x = 18
\][/tex]
[tex]\[
6x = 18
\][/tex]
- Divide both sides by 6:
[tex]\[
x = 3
\][/tex]
6. Find the Number of Pink Counters:
- Since there are [tex]\(3x\)[/tex] pink counters, substitute [tex]\(x = 3\)[/tex]:
[tex]\[
3x = 3 \times 3 = 9
\][/tex]
So, there are 9 pink counters in the bag.
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