Currently, you have $80 and your sister has $145. You decide to save $6 of your allowance each week, while your sister decides to spend her whole allowance plus $7 each week. How long will it be before you have as much money as your sister?
80 + 6x = 145 - 7x
13x = 65
x = 5
After 5 weeks both of you will have $110
To find out how long it will take for you to have as much money as your sister, we can set up a problem and solve it step by step.
First, let's calculate how much money your sister spends each week:
Your sister spends her whole allowance plus $7 each week, so her spending per week would be:
Sister's spending = her allowance + $7 = $145 + $7 = $152
Now, let's calculate how much money you save each week:
You save $6 of your allowance each week.
Now, let's calculate how much more money your sister has compared to you:
Difference in money = your sister's money - your money = $145 - $80 = $65
Since your sister's spending is greater than your saving, the difference in money between you and your sister will decrease each week.
To find out how long it will take for this difference to become zero (i.e., when you have as much money as your sister), we can divide the difference in money by the difference in saving and spending:
Time = Difference in money / (Difference in saving and spending) = $65 / ($6 + $152)
Now, let's calculate the time it will take:
Time = $65 / $158 ≈ 0.411
Therefore, it will take approximately 0.411 weeks for you to have as much money as your sister.