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?
A.) y-4=200(x-1700)
B.) y-1700=200(x-4)
C.) y-200=1700(x-4)
D.) y-1700=200(x+4)
y = amount at end of every week after 4 weeks = 1700 + 200 (x-4)
so
y - 1700 = 200(x-4)
To find the equation that models your savings account balance at the end of each week, we can analyze the given information.
Let's break down the information we have step by step:
1. You put $200 in your bank account each week.
2. After saving for 4 weeks, you have $1,700 in your account.
If we assume that "x" represents the number of weeks, we can use this information to form an equation.
Since you are putting $200 into your account each week, the amount of money in your account after "x" weeks can be represented as 200x.
Therefore, the equation will be of the form y = 200x, where "y" is the total amount of money in your account after "x" weeks.
Now, let's substitute the given information into this equation:
When x = 4, the total amount of money in your account is $1,700, so we can write the equation as follows:
1700 = 200(4)
Simplifying this equation, we find:
1700 = 800
However, this equation doesn't hold true, which means there must be an error in our calculation or analysis.
Let's analyze each answer choice and find the correct equation:
A.) y - 4 = 200(x - 1700)
B.) y - 1700 = 200(x - 4)
C.) y - 200 = 1700(x - 4)
D.) y - 1700 = 200(x + 4)
By comparing the equation with our step-by-step analysis, we can see that the correct equation is:
B.) y - 1700 = 200(x - 4)
This equation represents the savings account balance at the end of each week, where "y" is the total amount of money in the account and "x" is the number of weeks.
To solve this problem, we need to find the equation that models the savings account balance at the end of each week.
Let's analyze the given information:
- You save $200 in your bank account each week.
- After saving for 4 weeks, you have $1700 in your account.
Let's set up the equation:
We know that the starting balance is $0, and after 4 weeks, the balance is $1700. The amount saved each week is $200.
We can use the slope-intercept form of a linear equation, which is given by: y = mx + b, where m is the slope and b is the y-intercept.
The slope represents the rate of change, which in this case is $200 (the amount saved each week).
Given this information, the equation that models the savings account balance at the end of each week is:
y = 200x + b
To find the y-intercept (b), we can substitute the values from the given information. After 4 weeks, you have $1700 in your account. So we have:
1700 = 200(4) + b
Simplifying this equation, we find:
1700 = 800 + b
Subtracting 800 from both sides:
900 = b
Now, substitute the value of b back into the equation:
y = 200x + 900
Comparing this equation with the options given, we can see that the correct equation is:
C.) y - 200 = 1700(x - 4)