Question

David had $500 in his savings account when Sarah opened a savings account with $200.

David deposited $20 into his savings account each week.
Sarah deposited $50 into her savings account each week.
The accounts did not earn interest.
Which equation can be used to find x, the number of weeks it will take Sarah to save the same amount of money as David?
A. 500 + 50x = 200 + 20x
B. 500x + 20 - 200x + 50
C. 520x = 250x
D. 500 + 20x = 200 + 50x

Answer 1

The equation to find the number of weeks x for Sarah to have the same amount as David is 500 + 20x = 200 + 50x, which represents David's and Sarah's savings over time without interest.

Step-by-step explanation:

We want to find the equation that represents the number of weeks x it takes for Sarah to have the same amount of money in her savings account as David. Initially, David has $500 and Sarah has $200. Every week, David adds $20 to his savings, and Sarah adds $50 to hers. Since the accounts do not earn interest, we can use a simple linear equation to model the total amount of money each person has over time.

After x weeks, David's total amount will be his initial amount plus $20 times the number of weeks: 500 + 20x. Similarly, Sarah's total amount after x weeks will be her initial amount plus $50 times the number of weeks: 200 + 50x.

To find out when they will have the same amount, we set these two expressions equal to each other:

500 + 20x = 200 + 50x

This equation can be used to solve for x, representing the number of weeks needed for Sarah to save the same amount of money as David.