Currently, you have $160, and your brother has $290. You decide to save $6 of your allowance each week, while your brother spends $7 of his allowance each week. How long will it be before you have as much money as your brother?
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Let x = number of weeks
You have $160 and you are saving $6 a week. So after x weeks, you'll have 160+6x dollars.
Your brother has $290 and he's spending $7 a week. After x weeks, he will have 290-7x dollars
Set the two expressions equal to each other and solve for x.
160+6x = 290 - 7x
160+6x+7x = 290
6x+7x = 290-160
13x = 130
x = 130/13
x = 10
In 10 weeks, ie at week x = 10, you and your brother will have the same amount of money.
Both of you will have 160+6*10 = 160+60 = 220 dollars
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