College

Reece has some counters in a bag. [tex]4\%[/tex] of the counters are green, and [tex]40\%[/tex] of the counters are blue.

If 32 counters are green, how many counters are blue?

Answer :

To solve this problem, we'll work through it step-by-step:

1. Identify the given information:
- [tex]\(4\%\)[/tex] of the counters are green.
- [tex]\(40\%\)[/tex] of the counters are blue.
- There are 32 green counters.

2. Calculate the total number of counters:
- Since you know that [tex]\(4\%\)[/tex] of the total number of counters is 32 (the green counters), you can set up an equation to find the total number of counters.
- The formula for calculating the total number based on a percentage is:
[tex]\[
\text{Total counters} = \frac{\text{Number of green counters} \times 100}{\text{Green percentage}}
\][/tex]
- Plug in the given values:
[tex]\[
\text{Total counters} = \frac{32 \times 100}{4} = 800
\][/tex]

3. Calculate the number of blue counters:
- We know that [tex]\(40\%\)[/tex] of the total counters are blue.
- Now use the total number of counters to calculate the number of blue counters:
[tex]\[
\text{Number of blue counters} = \frac{40}{100} \times 800
\][/tex]
- Simplifying this gives:
[tex]\[
\text{Number of blue counters} = 320
\][/tex]

Therefore, there are 320 blue counters in the bag.

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