Question

Brittany opened a bank account and deposited some money. She then added the same amount of money each week to her bank account. The table shows the amount of money Brittany will have at the end of x weeks.


Brittany's Bank Account

Weeks 1 2 3 4
Amount (dollars) $112 $124 $136 $148

How much money did Brittany open her account with, and how much money did she deposit each week?
Responses
A Brittany opened the account with $12 and added $100 each week.Brittany opened the account with $12 and added $100 each week.
B Brittany opened the account with $25 and added $50 each week.Brittany opened the account with $25 and added $50 each week.
C Brittany opened the account with $100 and added $12 each week. Brittany opened the account with $100 and added $12 each week.
D Brittany opened the account with $50 and added $25 each week.

Answer 1

To find how much money Brittany opened her account with and how much she added each week, we can analyze the table given:

- **At Week 1**: Amount = $112
- **At Week 2**: Amount = $124
- **At Week 3**: Amount = $136
- **At Week 4**: Amount = $148

From the table, we can observe the amount increases by the same amount each week:

- From Week 1 to Week 2: $124 - $112 = $12
- From Week 2 to Week 3: $136 - $124 = $12
- From Week 3 to Week 4: $148 - $136 = $12

This indicates that the amount added each week is $12.

To find out how much Brittany started with, we can use the amount in Week 1 as follows:

Let \( S \) be the starting amount and \( r \) be the amount added each week. We have:

\[
S + r \cdot 1 = 112
\]
\[
S + 12 \cdot 1 = 112
\]

Solving this gives:

\[
S + 12 = 112 \implies S = 112 - 12 = 100
\]

Thus, Brittany opened her account with $100 and added $12 each week.

So the correct option is:

**C**: Brittany opened the account with $100 and added $12 each week.