Question

A bank offers two checking account plans. Plan A has a base service charge of $9.00 per month plus 7 cents per check. Plan B charges a base service charge for $1.00 per month plus 27 cents per check. For what number of checks per month will plan A be better than plan B?How would I write that in interval notation?

Answer 1

• The number of checks, c is greater than 40.

,

• (40, ∞)

Explanation:

Let the number of checks per month = c

Plan A

• Base service charge = $9.00 per month.

,

• Charge per check =7 cents = $0.07

The total cost for plan A is: 9+0.07c

Plan B

• Base service charge = $1.00 per month.

,

• Charge per check =27 cents = $0.27

The total cost for plan B is: 1+0.27c

For plan A to be better than plan B, the total cost for plan A must be less than the total cost for plan B. That is:

`9+0.07c<1+0.27c`

The inequality is solved for c.

`\begin{gathered} 9-1<0.27c-0.07c \\ 8<0.2c \\ \text{Divide both sides by 0.2} \\ (8)/(0.2)<(0.2c)/(0.2) \\ 4040 \end{gathered}`

Plan A will be better than Plan B whenever the number of checks is greater than 40.

This can be written in the interval notation as:

`(40,\infty)`