Lydia is comparing two checking accounts, one has a monthly fee of $10 and a per-check fee of $0.10, and the other has a monthly fee of $5 and a per-check fee of $0.25. What is the minimum number of checks Lydia needs to write for the first bank to be a better option?
you want n such that
10+0.10n < 5 + 0.25n
To determine the minimum number of checks Lydia needs to write for the first bank to be a better option, we'll compare the total cost of both options.
Let's define:
- x as the number of checks Lydia needs to write.
- C1 as the total cost for the first bank.
- C2 as the total cost for the second bank.
For the first bank:
- The monthly fee is $10.
- The per-check fee is $0.10.
- Therefore, the total cost for the first bank is C1 = $10 + ($0.10 * x).
For the second bank:
- The monthly fee is $5.
- The per-check fee is $0.25.
- Therefore, the total cost for the second bank is C2 = $5 + ($0.25 * x).
To find the minimum number of checks Lydia needs to write for the first bank to be a better option, we'll set up an inequality:
C1 < C2
$10 + ($0.10 * x) < $5 + ($0.25 * x)
Now, we can solve this inequality to find the minimum number of checks Lydia needs to write.
$10 - $5 < ($0.25 * x) - ($0.10 * x)
$5 < $0.15 * x
Dividing both sides of the inequality by $0.15:
$5 / $0.15 < x
x > 33.33333
Since the number of checks has to be a whole number, we need to round up to the next whole number. Therefore, the minimum number of checks Lydia needs to write for the first bank to be a better option is 34.