You started this year with $375 saved and you continue to save an additional $17 per month. Write an algebraic expression to represent the total amount of money saved after m months.
The correct answer and explanation is:
The algebraic expression that represents the total amount of money saved after mm months is: 375+17m375 + 17m
Explanation:
In this problem, you started the year with $375 saved. This is a fixed amount and does not change with time, so it is represented as the constant 375 in the algebraic expression.
Each month, you save an additional $17. Since this is a recurring monthly saving, the total additional amount saved after mm months is represented as 17m17m. The variable mm represents the number of months that have passed.
The two parts of the expression—375 (the initial amount saved) and 17m17m (the savings from the monthly contribution)—are added together to give the total amount saved after mm months.
For example, if 3 months have passed, you can substitute m=3m = 3 into the equation: 375+17(3)=375+51=426375 + 17(3) = 375 + 51 = 426
This means that after 3 months, the total amount saved would be $426.
If you wanted to calculate the total savings after 6 months, for instance, you would substitute m=6m = 6: 375+17(6)=375+102=477375 + 17(6) = 375 + 102 = 477
Thus, the algebraic expression allows you to calculate how much money has been saved at any given point in time, depending on how many months have passed. The expression is linear because the rate of saving is constant each month, which is typical for simple saving models.