how do I determine how to solve a problem like this
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
linear, as the amount remaining on the card decreases at a constant rate each month.
To determine how to solve this problem, you can follow these steps:
1. Identify the variables: In this case, the variables are the number of months after the first year (let's call it "m") and the amount remaining on the card.
2. Determine the starting value: The problem states that the starting value of the cash card is $25.
3. Identify the rate of decrease: The problem states that if the card is not used within the first year, the value decreases by $2.50 per month.
4. Write the mathematical equation for the relationship: Since the relationship is linear, you can use the slope-intercept form of a linear equation (y = mx + b) to represent it. The equation for the remaining amount on the card is: Amount Remaining = Starting Value - Rate of Decrease * Number of Months.
In this case, the equation becomes: Amount Remaining = $25 - $2.50 * m.
5. Use the equation to solve the problem: You can plug in different values for "m" (number of months after the first year) into the equation to find the corresponding remaining amount on the card. For example, if you want to know the remaining amount after 2 years (24 months), you can substitute m = 24 into the equation and calculate it as follows:
Amount Remaining = $25 - $2.50 * 24 = $25 - $60 = $-35.
In this case, the remaining amount is negative, indicating that the card has no value left after 2 years.
By following these steps, you can determine the amount remaining on the card for any given number of months after the first year.