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A bag contains red, blue, and orange counters. For every red counter, there are 6 blue counters. For every 2 blue counters, there are 5 orange counters. What is the ratio of red counters to orange counters? Give your answer in its simplest form.

Answer :

To find the ratio of red counters to orange counters, we need to first understand the relationships given in the problem:

  1. For every red counter, there are 6 blue counters.
  2. For every 2 blue counters, there are 5 orange counters.

Let's assign a variable to the number of red counters. Say the number of red counters is [tex]R = 1[/tex].

Since for each red counter there are 6 blue counters, the number of blue counters [tex]B[/tex] would be:

[tex]B = 6 \times R = 6 \times 1 = 6[/tex]

Now, for every 2 blue counters, there are 5 orange counters. Therefore, the number of orange counters [tex]O[/tex] would be:

Since [tex]B = 6[/tex], it can be divided into three groups of 2 blue counters each, so the calculation for respective orange counters is:

[tex]O = 5 \times \left( \frac{B}{2} \right) = 5 \times \left( \frac{6}{2} \right) = 5 \times 3 = 15[/tex]

Now, with these values:\

  • Red counters [tex]= 1[/tex] \
  • Orange counters [tex]= 15[/tex]

The simplest ratio of red to orange counters is:

[tex]\frac{1}{15}[/tex]

Thus, the ratio of red counters to orange counters is 1:15.

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