how do I determine how to solve a problem like this step by step?
A cash card has a starting value of $25. If the card is not used within the first year of its purchase, the value on the card begins to decrease by $2.50 per month.
The relationship between the number of months after the first year and the amount remaining on the card is Continuous or discrete?
To determine how to solve a problem like this step by step, you can follow these steps:
1. Read and understand the problem: Make sure you understand all the given information and what the problem is asking for.
2. Identify the variables: In this problem, the variable is the number of months after the first year and the amount remaining on the card.
3. Determine if the relationship is continuous or discrete: To do this, ask yourself if the variable can take on any value within a range or if it can only take on specific values. In this case, as the number of months after the first year can be any value (e.g., 13.5 months), the relationship is continuous.
4. Formulate the equation or expression: Based on the given information, you can write an equation or expression to represent the relationship between the number of months and the amount on the card.
5. Solve the problem: Use the equation or expression to solve the problem. Substitute the values given or ask you to find, and calculate the result.
In the case of the specific problem you provided:
1. The problem states that a cash card starts with a value of $25 and decreases by $2.50 per month after the first year.
2. The variables are the number of months after the first year and the amount remaining on the card.
3. The relationship is continuous because the number of months can take on any value (e.g., 13.5 months).
4. To formulate the equation or expression, you could use the equation: Amount remaining = Starting value - (decrease per month * number of months).
5. To find the amount remaining, substitute the given values into the equation. For example, after 2 years (24 months), the amount remaining would be calculated as $25 - ($2.50 * 24) = $25 - $60 = -$35. Note that a negative value indicates that the card has a debt.
In summary, to solve a problem like this step by step, you need to read and understand the problem, identify the variables, determine if the relationship is continuous or discrete, formulate the equation or expression, and solve the problem using the equation or expression.