Sam opened a savings account with $400. He earns $1,640 a month at his job and will deposit 3% of his monthly pay every month into his new savings account. Assuming he doesn't withdraw money from his savings account, which equation shows the balance [tex]$y$[/tex] of his savings account [tex]$x$[/tex] months after he opened it?
A. [tex]$y=12x+400$[/tex]
B. [tex]$y=49.2x+40$[/tex]
C. [tex]$y=0.03x+400$[/tex]
D. [tex]$y=400x+1640[/tex]
Answer (2)
Calculate the monthly deposit: 1640 × 0.03 = 49.2 .
Formulate the equation for the savings account balance: y = 49.2 x + 400 .
The equation represents the balance y after x months.
The final equation is y = 49.2 x + 400 .
Explanation
Understanding the Problem Let's analyze the problem. Sam starts with an initial deposit of $400 in his savings account. Each month, he deposits 3% of his monthly salary, which is $1 , 640 . We need to find an equation that represents the total balance y in his savings account after x months, assuming he makes no withdrawals.
Calculating Monthly Deposit First, we need to calculate the amount Sam deposits each month. This is 3% of his $1 , 640 salary. To find this, we multiply his salary by 0.03 : 1640 × 0.03 = 49.2 So, Sam deposits $49.2 each month.
Formulating the Equation Now, we can write the equation for the balance y in his savings account after x months. He starts with $400 , and adds $49.2 each month. So, the equation is: y = 49.2 x + 400 This equation represents the total balance y as the sum of his initial deposit and the total amount he has deposited over x months.
Final Answer Therefore, the equation that shows the balance y of his savings account x months after he opened it is y = 49.2 x + 400 .
Examples
Imagine you're saving up for a new gaming PC that costs $1200 . If you start with $400 and save $49.2 each month, this equation helps you calculate how many months it will take to reach your goal. By setting y = 1200 , you can solve for x to find the number of months needed. This kind of calculation is useful for planning any savings goal, from buying electronics to saving for a down payment on a car.
The equation that represents the balance y of Sam's savings account after x months is y = 49.2 x + 400 . This equation accounts for his initial deposit and his monthly deposits of 49.20. T h u s , t h ecorrec t o pt i o ni s B : y = 49.2x + 400$.
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