Chris has $100 in his savings account and he adds $20 a month to the account. The total amount can be represented by the linear function T = 20x + 100. His goal is to have a total of $300 in four more months. What should he change in the function to reach this goal?
Change the amount he adds each month to $50
To reach the goal of having a total of $300 in four more months, we need to find what value we should change in the linear function T = 20x + 100.
Let's break down the problem step by step:
Step 1: Understand the given information
- Chris currently has $100 in his savings account.
- Chris adds $20 to the account each month.
- The total amount in the account can be represented by the linear function T = 20x + 100, where T represents the total amount and x represents the number of months.
Step 2: Determine the expression for the future value
- We want to find the total amount in the account after four more months.
- So, we need to substitute x + 4 for x in the linear function to get the new expression for the future value.
- The new expression will be T = 20(x + 4) + 100.
Step 3: Simplify the expression
- Distribute the 20 across the parentheses: T = 20x + 80 + 100.
- Combine like terms: T = 20x + 180.
Step 4: Set up the equation for the goal
- The goal is to have a total of $300 in the account after four more months.
- So, we set up the equation T = 300.
Step 5: Solve the equation
- Set the expression for the future value, 20x + 180, equal to the goal, 300: 20x + 180 = 300.
- Subtract 180 from both sides of the equation: 20x = 120.
- Divide both sides of the equation by 20: x = 6.
Step 6: Determine what should be changed in the function
- In the original linear function T = 20x + 100, we need to find what value should be changed to reach the goal.
- From our calculations, we found that the value of x (number of months) should be 6 to reach the goal of having $300 in four more months.
Therefore, to change the function to reach this goal, Chris needs to update the expression to T = 20(6) + 100, which simplifies to T = 220.