Checking account earnings at Baker's Bank are expressed by the equation: I = - 0.09x + 10.2 While the earnings at Elite Bank are modeled by: I = - 0.02x + 7.5 In both cases, x is the number of checks written. At what number of checks will Elite Bank start generating more checking account income than Baker's Bank? (1 point)

Question

12
25
39
42

Answer 1

To find the number of checks at which Elite Bank will start generating more checking account income than Baker's Bank, we need to set the earnings equations equal to each other and solve for \( x \):

1. Equations:

   • Baker's Bank: \( I_B = -0.09x + 10.2 \)
   • Elite Bank: \( I_E = -0.02x + 7.5 \)

2. Set the equations equal: \[ -0.09x + 10.2 = -0.02x + 7.5 \]

3. Rearrange the equation: \[ 10.2 - 7.5 = -0.02x + 0.09x \] \[ 2.7 = 0.07x \]

4. Solve for \( x \): \[ x = \frac{2.7}{0.07} \approx 38.57 \]

Since we are looking for the first whole number greater than this, we round up to 39.

Thus, Elite Bank starts generating more checking account income than Baker's Bank when 39 checks are written.

The answer is \(\text{39}\).