Question

A student has a savings account with $475 in it.

She deposits $125 of her paycheck into the account
every week. Her goal is to save $7,000 for college.
To do: Write an equation that represents the
relationship between the dollar amount in her account
and the number of weeks of saving. NOTE:
Let x = number of weeks since the initial deposit
Let y = total amount in the account a) y = 475x + 125
b) y = 125x + 475
c) y = 475 + 125x
d) y = 7,000 - 125x

Answer 1

The correct equation that represents the relationship between the dollar amount in the student's savings account and the number of weeks of saving is y = 125x + 475, where x is the number of weeks since the initial deposit and y is the total amount in the account.

Step-by-step explanation:

To write an equation that represents the relationship between the dollar amount in the student's savings account and the number of weeks of saving, we use the initial amount in the account as the starting point and add the consistent weekly deposits to it. The initial amount is $475, so that is our starting value or y-intercept.

The student deposits $125 every week, which is added to the initial amount. This is the slope of our linear equation. The number of weeks of saving is our variable, which we represent with x. Thus, for each week (x), the amount in the savings account increases by $125.

Combining these, we get the equation y = 125x + 475 where y is the total amount in the account after x weeks. This choice corresponds with option B from the given list.

This equation illustrates a fundamental principle of financial growth: Starting with an initial sum and regularly contributing a fixed amount can lead to a sizable savings over time. This principle is reflective of the power of consistent saving and is a cornerstone of personal financial planning.