In a group of 50 traders, 30 sell gari, and 40 sell rice. Each trader sells at least one of the two items. How many traders sell both gari and rice?
Understand the Problem
The question is asking how many traders in a group of 50 sell both gari and rice. It provides the total number of traders selling each item and implies that each trader sells at least one of the two items, so we need to find the intersection of the two sets.
Answer
The number of traders who sell both gari and rice is $20$.
Answer for screen readers
The number of traders who sell both gari and rice is ( 20 ).
Steps to Solve
- Define the sets Let:
- ( G ) = Number of traders selling gari = 30
- ( R ) = Number of traders selling rice = 40
- ( N ) = Total number of traders = 50
- ( x ) = Number of traders selling both gari and rice
-
Use the principle of inclusion-exclusion The principle states: $$ |G \cup R| = |G| + |R| - |G \cap R| $$ Where ( |G \cup R| ) is the number of traders selling at least one of the items, which is equal to the total number of traders ( N ).
-
Set up the equation Substituting in the known values: $$ 50 = 30 + 40 - x $$
-
Solve for ( x ) Rearranging the equation gives: $$ x = 30 + 40 - 50 $$
-
Calculate the value of ( x ) So, $$ x = 70 - 50 = 20 $$
The number of traders who sell both gari and rice is ( 20 ).
More Information
This problem involves basic principles of set theory, specifically the use of the inclusion-exclusion principle to find the intersection of two sets. Such problems are common in probability and statistics.
Tips
- Confusing the total number of traders with those selling only one item.
- Forgetting to account for the intersection properly in inclusion-exclusion.
AI-generated content may contain errors. Please verify critical information
