Question

Yesterday, two friends went into a bank to open savings accounts. Tim started by putting $1 in his account, and he will deposit an additional $319 each week. Linda made no initial deposit, but she will add $320 more each week. In a few weeks, the friends will have the same account balance. What is that account balance

Answer 1

After setting up equations for both Tim and Linda's account balances and setting them equal, it's determined that they will both have the same account balance of $320 after 1 week.

Step-by-step explanation:

The student is asking about a scenario where two friends, Tim and Linda, are opening savings accounts with different initial deposits and weekly deposit amounts. Tim starts with $1 and adds $319 each week, while Linda starts with $0 but adds $320 each week. The question is to find at what account balance they will be equal.

Let's denote Tim's balance after n weeks as T_n and Linda's balance as L_n. We can set up the equations as follows:

T_n = 1 + 319n

L_n = 320n

We want to find when T_n is equal to L_n. Setting the equations equal to each other gives us:

1 + 319n = 320n

Subtracting 319n from both sides, we get:

1 = n

This tells us that after 1 week, both Tim and Linda will have the same amount in their accounts. Now we can substitute n back into either equation to find the balance:

Account Balance = 320 * 1 = $320

After 1 week, Tim and Linda will both have a balance of $320 in their savings accounts.