You have $22 in your bank account, and you deposit $11.50 per week. Your cousin has $218 in his bank account and is withdrawing $13 per week. The graph of this problem situation intersects at x=8. What does this mean?
A.
In 8 weeks, you will have triple the amount of money in your account.
B.
In 8 weeks, your cousin will run out of money.
C.
In 8 weeks, both bank accounts will have the same amount of money in them.
D.
In 8 weeks, you will break-even.
If the graphs intersect, their values are equal at that point.
C. In 8 weeks, both bank accounts will have the same amount of money in them.
To determine what the intersection at x=8 means, we need to understand what x represents in this context. In this problem situation, x refers to the number of weeks that have passed.
The given information tells us that you deposit $11.50 per week and your cousin withdraws $13 per week. By subtracting the weekly withdrawal amount from the weekly deposit amount, we can calculate the net change in money for each person per week.
For you, the net change in money per week is: $11.50 - $0 = $11.50 (as you are only depositing)
For your cousin, the net change in money per week is: -$13 (as he is only withdrawing)
Now, let's analyze the options based on this information:
A. In 8 weeks, you will have triple the amount of money in your account.
Since you are only depositing money without any additional factors mentioned, your account balance would increase by $11.50 per week. Therefore, after 8 weeks, you would have: $22 + ($11.50 * 8) = $22 + $92 = $114. This does not align with the statement, so option A is not correct.
B. In 8 weeks, your cousin will run out of money.
Since your cousin withdraws $13 per week without depositing any money, his account balance would decrease each week. After 8 weeks, he would have: $218 - ($13 * 8) = $218 - $104 = $114. This also does not align with the statement, so option B is not correct.
C. In 8 weeks, both bank accounts will have the same amount of money in them.
To determine if the two bank accounts will have the same amount of money after 8 weeks, we need to calculate the respective balances. After 8 weeks, your account balance would be $22 + ($11.50 * 8) = $22 + $92 = $114. We already calculated that your cousin's balance would also be $114 after 8 weeks. Therefore, the statement aligns with the intersection at x=8, so option C is correct.
D. In 8 weeks, you will break-even.
"Breaking even" means that your account balance remains the same. However, we found that after 8 weeks, your account balance would increase to $114. Therefore, option D is not correct.
Based on the analysis, the correct answer is option C: In 8 weeks, both bank accounts will have the same amount of money in them.