Question

Yesterday, two friends went into a bank to open savings accounts. Megan started by putting $80 in her account, and she will deposit an additional $15 each week. Noah made no initial deposit, but he will add $25 more each week. In a few weeks, the friends will have the same account balance.

Answer 1

8 weeks

Explanation:

We are to find the number of weeks that they will have the same account balance.

Let the number of weeks be x.

Megan started by putting $80 in her account, and she will deposit an additional $15 each week. This means after x weeks, she will have:

80 + 15x

Noah made no initial deposit, but he will add $25 more each week. After x weeks, he will have:

25x

To find the number of weeks for their amounts to be the same, we equate their amounts to one another:

80 + 15x = 25x

Collexting like terms and solving for x:

80 = 25x - 15x

80 = 10x

=> x = 80 / 10 = 8 weeks

After 8 weeks, the money in their accounts will be the same.