To determine how many checks you would need to write per month for the fees of checking account A and checking account B to be equal, we need to set up and solve the equations representing the total monthly cost for each account.
Let's define:
- [tex]\( x \)[/tex] as the number of checks written per month.
For checking account A:
- The monthly fee is [tex]$10.
- The per-check fee is $[/tex]0.25.
The total monthly cost for account A can be expressed as:
[tex]\[ \text{Cost}_A = 10 + 0.25x \][/tex]
For checking account B:
- The monthly fee is [tex]$14.
- The per-check fee is $[/tex]0.09.
The total monthly cost for account B can be expressed as:
[tex]\[ \text{Cost}_B = 14 + 0.09x \][/tex]
We want to find the number of checks [tex]\( x \)[/tex] where these costs are equal:
[tex]\[ 10 + 0.25x = 14 + 0.09x \][/tex]
To solve this equation:
1. Subtract 10 from both sides:
[tex]\[ 0.25x = 4 + 0.09x \][/tex]
2. Subtract 0.09x from both sides:
[tex]\[ 0.25x - 0.09x = 4 \][/tex]
[tex]\[ 0.16x = 4 \][/tex]
3. Divide both sides by 0.16 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{4}{0.16} \][/tex]
[tex]\[ x = 25 \][/tex]
Therefore, you would need to write 25 checks per month for the fees of checking account A and checking account B to be equal.
