Question

You have $134 in a savings account and save $10

per week. Your friend has $85 in a savings account
and saves $17 per week. How many weeks will it
take for you and your friend to have the same
balance?

Answer 1

By setting up equations based on the initial savings and the weekly savings rates, we find that it will take 7 weeks for both parties to have the same amount in their savings accounts.

Step-by-step explanation:

The question revolves around figuring out when two people saving money at different rates will arrive at the same account balance. To find when you and your friend will have the same balance in your savings accounts, we need to set up an equation. You start with $134 and save $10 per week, while your friend starts with $85 and saves $17 per week.

We can express these situations with the equations:

• Your savings after x weeks: 134 + 10x
• Your friend's savings after x weeks: 85 + 17x

To find the number of weeks when both of you will have the same amount, we need to set these two equations equal to each other:

134 + 10x = 85 + 17x

Solving for x, we subtract 10x from both sides:

134 = 85 + 7x

and then subtract 85 from both sides:

49 = 7x

Finally, divide both sides by 7 to isolate x:

x = 7

Thus, it will take 7 weeks for both of you to have the same amount in your savings accounts.