Question

1. Fatima has $207 in her account. A $7.25 fee is charged each month the balance is below $100.

She withdraws $120 one time.

a. Write an equation to model her balance after x months since the withdrawal, if she makes no
further deposits or withdrawals.


b. Solve for y when x=4. What does that mean in this context?


c. After how many months will Fatima's balance reach $0 or below?

Answer 1

a. y=87-7.25x

b. y= 58, amount of money she will have in four months

c. 12 months

Explanation:

So First, since she removed 120 dollars from her 207, we need to minus 120 from 207

207-120=87

So she has 87 dollars in her account, which means that she needs is going to get charged 7.25 a month. If x equals the amount of months, and y equals the total amount of money in her bank account, that means that every month she will get another 7.25 taken away from her bank account. We can write that equation like this:

y=87-7.25x

The Next problem is to solve for how much money she has after four months. We simply just plug in the number for x like so:

y=87-7.25(4)

And solve

y=87-7.25(4)

-7.25*4=-29

y=87-29

87-29=58

y=58

So she will have 58 dollars left in her bank account, because y equals the amount in her bank account.

The next problem asks when Fatima's bank account will be 0 or below, so plug in zero for y

y=0

0=87-7.25x

Then solve

0=87-7.25x

-87 -87

-87=-7.25x

/-7.25 /-7.25

12=x

In twelve months she will have zero dollars in her bank account, since x represents months.

Answer 2

Explanation:

a. Let's first calculate Fatima's balance after the withdrawal.

Starting balance = $207

Withdrawal amount = $120

Balance after withdrawal = $207 - $120 = $87

Now, we need to consider the monthly fee of $7.25 that is charged if the balance is below $100. If the balance is at or above $100, there is no fee.

Let Y be the balance in dollars and X be the number of months since the withdrawal. Then the equation that models Fatima's balance after X months is:

Y = 87 - 7.25X if 0 <= Y < 100

Y = 87 if Y >= 100

Note that the balance can never be negative in this case, so we only need to consider the case when the balance is below $100.

b. To solve for Y when X=4, we plug in X=4 into the equation we derived in part (a):

Y = 87 - 7.25X

Y = 87 - 7.25(4)

Y = 87 - 29

Y = 58

So after 4 months since the withdrawal, Fatima's balance will be $58.

c. We want to find when the balance reaches $0 or below. We can use the equation we derived in part (a) and set Y to 0:

0 = 87 - 7.25X

Solving for X, we get:

X = 87/7.25

X ≈ 12

So after 12 months since the withdrawal, Fatima's balance will reach $0.