Question

question 4 of 10
dewayne is comparing two checking accounts. one has a monthly fee of $7 and a per-check fee of $0.30, and the other has a monthly fee of $4 and a per-check fee of $0.40. what is the minimum number of checks dewayne needs to write for the first bank to be a better option?
a. 29
b. 31
c. 30
d. 28

Explanation:

Step1: Define Variables

Let \( x \) be the number of checks. The cost for the first bank is \( C_1 = 7 + 0.30x \), and for the second bank is \( C_2 = 4 + 0.40x \).

Step2: Set Up Inequality

We want \( C_1 < C_2 \), so \( 7 + 0.30x < 4 + 0.40x \).

Step3: Solve Inequality

Subtract \( 0.30x \) and 4 from both sides: \( 7 - 4 < 0.40x - 0.30x \), which simplifies to \( 3 < 0.10x \).
Divide both sides by 0.10: \( x > \frac{3}{0.10} = 30 \).
Since \( x \) must be an integer, the minimum number of checks is 31.

Answer:

B. 31