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?

y – 4 = 200(x – 1,700)
y – 200 = 1,700(x – 4)
y – 1,700 = 200(x – 4)
y – 1,700 = 200(x + 4)
Mathematics

Answer 1

the third choice y-1700=200(x-4)

Answer 2

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

Explanation:

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

⇒d=200

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

⇒
`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)`

Substitute the values of
`d=200\ and\ a_4=1700` in above equation we get,

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