Question

a phone company offers two monthly charge, in Plan a, the customer pays a monthly fee of $40.10 and then an additional 4 cents per minute of use. In plan b, the Customer pays a monthly fee of $35 and then an additional 7 cents per minute of use. for what amounts of monthly phone use will plan a cost no more than Plan B

Answer 1

x > 1.7 minutes

The monthly telephone usage amounts so that plan A is not greater than plan B are all greater than 1.7 minutes.

Explanation:

The two plans must be defined by the equation of the line y = mx + b, where

y = plan

m = slope or payment of additional cents per minute

x = time expressed in minutes

For Plan A, we have

y = 4x + 40.10 (Equation A)

While plan B is defined as

y = 7x + 35 (Equation B)

Plan A must be less than Plan B,

4x + 40.10 < 7x + 35

We put the “x” on the left side and the independent terms on the right side,

4x - 7x < 35 - 40.10

We add algebraically,

-3x < -5.10

We multiply the equation by -1 to eliminate the two “minus” signs, changing the inequality sign,

3x > 5.10

We isolate x,

x > 5.10 / 3

We solve, calculating the value of x,

x > 1.7 minutes

The monthly telephone usage amounts so that plan A is not greater than plan B are all greater than 1.7 minutes.