for 5 monthly checks, both banks charge the same amount.
for x < 5, Bank B charges less.
for x > 5, Bank A charges less.
Bank A charges a fixed fee of $5.00 plus $0.15 per-check fee.
So, if you do x monthly checks, Bank A will charge you:
A(x) = $5.00 + $0.15*x
Bank B charges a service fee (fixed) of $2.50 plus $0.35 per check, then for x monthly checks they charge:
B(x) = $2.50 + $0.35*x
Both banks will charge the same amount when:
A(x)= B(x)
So we need to solve the linear equation:
$5.00 + $0.15*x = $2.50 + $0.35*x
$5.00 - $2.50 = $0.35*x + $0.15*x
$2.50 = $0.50*x
$2.50/$0.50 = x = 5
So, for 5 monthly checks, both banks charge the same amount.
for x < 5, Bank B charges less.
for x > 5, Bank A charges less.
If you want to learn more about linear equations:
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