Question

question 7 of 10
bank a charges a monthly service fee of $2.00 and a per - check fee of $0.05, while bank b charges a monthly service fee of $1.50 and a per - check fee of $0.10. which of these numbers of monthly checks will cause bank a to charge less in fees than bank b?
a. 8
b. 9
c. 10
d. 11

Explanation:

Step1: Define fee equations

Let $x$ = number of checks.
Bank A fee: $2.00 + 0.05x$
Bank B fee: $1.50 + 0.10x$

Step2: Set up inequality for Bank A < Bank B

$$2.00 + 0.05x < 1.50 + 0.10x$$

Step3: Rearrange to isolate $x$

Subtract $1.50 + 0.05x$ from both sides:
$$2.00 - 1.50 < 0.10x - 0.05x$$
$$0.50 < 0.05x$$

Step4: Solve for $x$

$$x > \frac{0.50}{0.05} = 10$$
This means Bank A is cheaper when fewer than 10 checks are written. From the options, only 8 is less than 10.

Answer:

A. 8