Question

To save money, you put $200 in your bank account each week. After saving for 4 weeks, you have $1,700$ dollars in your account. Which equation models your savings account balance at the end of each week?

Answer 1

The given question is incomplete, here is a complete question.

To save money, you put $200 in your bank account each week. After saving for 4 weeks, you have $1,700$ dollars in your account. Which equation models your savings account balance at the end of each week?

(1) y – 4 = 200(x – 1,700)

(2) y – 200 = 1,700(x – 4)

(3) y – 1,700 = 200(x – 4)

(4) y – 1,700 = 200(x + 4)

Answer : The correct option is, (3) y – 1,700 = 200(x – 4)

Step-by-step explanation :

This question is solved by Arithmetic progression.

Given: To save money, you put $200 in your bank account each week. That means,

⇒ d = 200

After saving for 4 weeks, you have $1,700 dollars in your account. That means,

⇒
`a_4=1700`

Let
`a_1` be the initial amount in the bank.

then,

`a_4=a_1+3d\\\\\Rightarrow\ a_1=a_4-3d`

Now, Let 'x' be the number of weeks and 'y' be the savings account balance at the end of each week.

Then by Arithmetic Progression,

`y=a_1+d(x-1)\\\\\Rightarrow\ y=(a_4-3d)+d(x-1)\\\\\Rightarrow\ y=a_4-3d+dx-d\\\\\Rightarrow\ y-a_4=dx-4d\\\\\Rightarrow\ y-a_4=d(x-4)`

Now substitute the values of d = 200 and
`a_4=1700` in above equation we get:

`y-1700=200(x-4)`

Thus, the equation models your savings account balance at the end of each week is,
`y-1700=200(x-4)`

Answer 2

Let's say the savings in your account are given by $V, the number of weeks by n and the starting balance by $x:
V = x + 200n

Now if after saving for 4 weeks you have $1700 in your account, then:
1700 = x + 200*4
1700 = x + 800
x = 900, thus your starting balance is $900

Using this information we can now write up the general equation for the savings at the end of each week:
V = 900 + 200n