Answer :
To find the total number of counters in the bag, we need to use the given ratio of red to green counters, which is 2:3, and the fact that there are 28 red counters.
Here's the step-by-step solution:
1. Understand the Ratio: The ratio 2:3 means for every 2 red counters, there are 3 green counters.
2. Find the Ratio Multiplier: To determine how many times this ratio occurs in the bag, divide the actual number of red counters by the red part of the ratio:
[tex]\[
\text{Ratio Multiplier} = \frac{\text{Number of Red Counters}}{\text{Red Part of Ratio}} = \frac{28}{2} = 14
\][/tex]
3. Calculate the Number of Green Counters: Multiply the ratio multiplier by the green part of the ratio to find the number of green counters:
[tex]\[
\text{Number of Green Counters} = \text{Green Part of Ratio} \times \text{Ratio Multiplier} = 3 \times 14 = 42
\][/tex]
4. Calculate the Total Number of Counters: Add the number of red and green counters together to find the total number of counters:
[tex]\[
\text{Total Number of Counters} = 28 (\text{red}) + 42 (\text{green}) = 70
\][/tex]
So, the total number of counters in the bag is 70.
Here's the step-by-step solution:
1. Understand the Ratio: The ratio 2:3 means for every 2 red counters, there are 3 green counters.
2. Find the Ratio Multiplier: To determine how many times this ratio occurs in the bag, divide the actual number of red counters by the red part of the ratio:
[tex]\[
\text{Ratio Multiplier} = \frac{\text{Number of Red Counters}}{\text{Red Part of Ratio}} = \frac{28}{2} = 14
\][/tex]
3. Calculate the Number of Green Counters: Multiply the ratio multiplier by the green part of the ratio to find the number of green counters:
[tex]\[
\text{Number of Green Counters} = \text{Green Part of Ratio} \times \text{Ratio Multiplier} = 3 \times 14 = 42
\][/tex]
4. Calculate the Total Number of Counters: Add the number of red and green counters together to find the total number of counters:
[tex]\[
\text{Total Number of Counters} = 28 (\text{red}) + 42 (\text{green}) = 70
\][/tex]
So, the total number of counters in the bag is 70.
