To determine the number of months, [tex]\( m \)[/tex], it will take for both the International Business Club (IBC) and the Future Agricultural Leaders Club (FALC) to have the same amount of money, we need to set up an equation based on their respective starting balances and monthly expenditures.
1. Starting Balances:
- IBC starts with \[tex]$250.50.
- FALC starts with \$[/tex]300.00.
2. Monthly Expenditures:
- IBC spends \[tex]$35.00 each month.
- FALC spends \$[/tex]45.25 each month.
3. Balancing Equations After [tex]\( m \)[/tex] Months:
- The balance for IBC after [tex]\( m \)[/tex] months can be expressed as:
[tex]\[
\text{Balance}_{\text{IBC}} = 250.5 - 35m
\][/tex]
- The balance for FALC after [tex]\( m \)[/tex] months can be expressed as:
[tex]\[
\text{Balance}_{\text{FALC}} = 300 - 45.25m
\][/tex]
To find the point at which both clubs have the same amount of money remaining in their accounts, we set the two expressions equal to each other:
[tex]\[
250.5 - 35m = 300 - 45.25m
\][/tex]
This equation correctly sets up the balance conditions after [tex]\( m \)[/tex] months for both clubs. Thus, the equation which can be used to find [tex]\( m \)[/tex] is:
[tex]\[
250.5 - 35m = 300 - 45.25m
\][/tex]
