Write and equation that represents this situation.

Question

Diana has $150 in her savings account and is depositing $50 each month. Sarah has $250 in her savings account and depositing $10 each month. Let m stand for the number of months and t for the total amount in their savings account.

Answer 1

Hi Svetlana! For this problem, both Diana and Sarah's situations can be represented by linear equations of the form y = mx + b, where m is the slope, b is the y-intercept (starting value), x is the independent variable (input), and y is the dependent variable (output). The variable y is dependent on the variable x. In our case, m represents the number of months and t represents the total amount of money in the savings account. The total amount of money in the savings accounts is dependent on the number of months that have passed, since each month, both Diana and Sarah deposit money into their account, causing the total number of savings to increase. Therefore, the total amount of money in the savings account, t, is our dependent variable (y in the y = mx + b equation), and the number of months, m, is our independent variable (x in the y = mx + b equation).

1) Diana's situation

Diana's savings account starts off with $150. This amount is fixed and represents her starting value (the "b" in the y = mx + b equation). She deposits $50 per month, and we can represent the number of months with m.. Since Diana deposits $50 each month, and our number of months is represented with m, we can represent this as 50m. This is the "mx" part of the linear equation, and represents $50 times the number of months m. Combining everything, we have our equation, which looks like this:

t = 50m + 150

This is the linear equation which represents the total savings, t, in Diana's account for a certain number of months, m.

2) Sarah's situation

Sarah starts off with $250 in her savings account. This is the starting value (the "b" in the y = mx + b equation). Since she deposits $10 per month, we can represent this by 10m (the "mx" in the y = mx + b equation). This is $10 times the number of months m. Combining all of this, we have our linear equation:

t = 10m + 250

This is the linear equation representing the total savings, t, in Sarah's account for a certain number of months, m.