Question

At the end of the summer, Caitlin had saved $120 from her summer job. This was her initial deposit into a new savings account at the bank. As the school year starts, Caitlin is going to deposit another $5 each week from her allowance. Is her account balance proportional to the number of weeks of deposits? Explain your reasoning.

Answer 1

Let X be the number of weeks she deposits money.

The equation to solve for the account balance would be 120 + 5x ( She started with 120 dollars and is adding 5 dollars per week)

week 1: balance = 120 +5(1) = $125

week 2: balance = 120 +5(2) = $130

week 3: balance = 120 + 5(3) = $135

week 4: balance = 120 +5(4) = $140

Now to see if it proportional divide each total by the number of weeks:

week 1: 125 / 1 = 125

week 2: 130 / 2 = 65

week 3: 135 / 3 = 45

week 4: 140 / 4 = 35

Find the difference between the weeks:

Week 1 & 2 : 125 - 65 = 60

Week 2 & 3: 65 -45 - 20

Week 3 & 4: 45 -35 = 10

Since the 3 differences are not the same, the balance is not proportional to the number of weeks.