Question

Davis and Shannon are saving money. Davis had $200 in his account and is saving $10 each week. Shannon started with $250 in her account and is saving $5 each week. After how many weeks will Davis and Shannon have the same amount? Write and solve an equation to answer the question.

Answer 1

Davis and Shannon will have the same amount saved after 10 weeks by setting up linear equations based on their savings rate and starting amounts, and then solving for the number of weeks.

Step-by-step explanation:

To solve the problem where Davis and Shannon are saving money, we need to set up an equation for each person and determine after how many weeks they will have the same amount of money. We let w represent the number of weeks.

Davis starts with $200 and saves $10 each week, so his savings can be represented as:

200 + 10w

Shannon starts with $250 and saves $5 each week, so her savings can be represented as:

250 + 5w

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

200 + 10w = 250 + 5w

To solve for w, we first subtract 5w from both sides:

200 + 5w = 250

Then, we subtract 200 from both sides:

5w = 50

Finally, we divide both sides by 5 to find w:

w = 10

Therefore, after 10 weeks, Davis and Shannon will have the same amount of money saved.