Evaluate financial decisions using mathematical reasoning

Detailed Explanation: Evaluate financial decisions using mathematical reasoning

A good financial decision compares the total cost of each option, not just one price. Follow these steps:

1. Identify the fixed cost and the cost that changes.
2. Use the same amount of use for each option.
3. Calculate each total cost.
4. Compare the totals with your budget.
5. Choose the option that best fits your needs.

Example

You are choosing a texting plan.

• Plan A: $12 per month plus $0.10 per text
• Plan B: $25 per month with unlimited texts
• You expect to send $(180)$ texts each month.
• Your monthly budget is $28.

Step 1: Write a cost rule for each plan.

For Plan A, the total cost is

where $t$ is the number of texts.

Plan B always costs

because it has unlimited texts.

Step 2: Substitute your expected use.

For Plan A:

For Plan B:

Step 3: Compare the costs and the budget.

Plan B costs $5 less:

Plan A costs $30, which is more than your $28 budget. Plan B costs $25, which is within your budget.

Step 4: Make the decision.

Choose Plan B. It is both cheaper for $(180)$ texts and affordable within the budget.

You can also find when the plans cost the same by setting their costs equal:

Subtract $(12)$:

Divide by $(0.10)$:

The plans cost the same at $(130)$ texts. If you send more than $(130)$ texts, Plan B is cheaper; if you send fewer than $(130)$, Plan A is cheaper.