Modeling

There are many situations where simultaneous equations are needed to solve real-world problems. Some of those examples are below:

1. Deciding whether an item is cheaper to buy online with additional shipping costs or to buy it locally.
2. Deciding whether joining a CD music club which requires a monthly purchase is more cost effective than purchasing them when wanted.
3. Deciding which phone plan is cheaper.

Anne is trying to choose between two phone plans. The first plan, with Vendafone costs $20 per month, with calls costing an additional 25 cents per minute. The second company, Sellnet, charges $40 per month, but calls cost only 8 cents per minute. Which should she choose?

y = total cost of the plan and x = number of minutes

Vendafone: y = 0.25x + 20

Sellnet: y = 0.08x + 40

The following is a graph representing the situation.

The intersection point is (117.65, 49.41)