High School

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Siena opens a bank account with $45 and adds $8 to the account each week. On the same day, Warren opens an account with $38 and adds $9 to the account each week. They are both saving $400 for a new laptop.

Which question can be answered by solving the equation [tex]45 + 8w = 38 + 9w[/tex], where [tex]w[/tex] is the number of weeks Siena and Warren are saving?

a. After how many weeks will Siena and Warren have the same amount in their accounts?
b. How many more weeks will Siena have to save than Warren to have enough money to buy a laptop?
c. After how many weeks will Siena and Warren have enough money to buy their laptops?
d. How many more weeks will Warren have to save than Siena to have enough money to buy a laptop?

Answer :

Final answer:

By solving the equation 45 + 8w = 38 + 9w, we find that after 7 weeks, Siena and Warren will have the same amount in their accounts, which answers option (a) of the multiple-choice question provided. So, the correct answer is a. After how many weeks will Siena and Warren have the same amount in their accounts?

Explanation:

The student's question can be answered by solving the equation 45 + 8w = 38 + 9w, where w represents the number of weeks. This equation can be solved to find out after how many weeks Siena and Warren will have the same amount in their accounts. The equation simplifies when you subtract 8w from both sides, giving 45 = 38 + w, and then subtracting 38 from both sides to get w = 7. This means that after 7 weeks, Siena and Warren will have saved the same amount of money.

To answer the multiple-choice question, option (a) After how many weeks will Siena and Warren have the same amount in their accounts? is the correct one. We are looking for the point in time when both Siena's and Warren's savings equal each other, and this is precisely what the given equation represents.

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