Sure, let's solve this step-by-step to find out how many pears there are given the total number of fruits and the ratio of oranges to pears.
1. Understand the Ratio:
The ratio of oranges to pears is 3:2, meaning for every 3 oranges there are 2 pears.
2. Define the Total Number of Parts in the Ratio:
Adding the parts of the ratio together gives us the total number of "parts."
[tex]\[
\text{Total parts} = 3 (\text{parts of oranges}) + 2 (\text{parts of pears}) = 5
\][/tex]
3. Determine the Value of Each Part:
Given that the total number of fruits is 210, we need to find out how many fruits each "part" represents. We divide the total number of fruits by the total number of parts.
[tex]\[
\text{Value of each part} = \frac{\text{Total fruits}}{\text{Total parts}} = \frac{210}{5} = 42
\][/tex]
4. Calculate the Number of Pears:
Since the ratio tells us that there are 2 parts of pears, we multiply the value of each part by 2.
[tex]\[
\text{Number of pears} = \text{Value of each part} \times 2 = 42 \times 2 = 84
\][/tex]
So, the number of pears in the shop is 84.
