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Suppose you have \$28.00 in your bank account and start saving \$18.25 every week. Your friend has \$161.00 in his account and is withdrawing \$15 every week. When will your account be the same?

• math -

let amount1 = 28 - 18.25w
let amount2 = 161 - 15w

so you want amount1 = amount2
28 - 18.25w = 161 - 15w
-3.25w = 133

oops, a negative number of weeks ????

• math -

• math -

your money = \$28 + (\$18.25 * each week)
the \$28 is money that you already have in your bank account, and \$18.25 how much it will increase by each week.

friend's money = \$161 - (\$15 * each week)
the \$161 is money your friend has in his bank account, and \$15 is how much it will decrease by each week (which is why there is a minus sign)

you want to know which week you and your friend will have the same amount of money, so make your equations equal to one another.

let's call the week, say, "x".

\$28 + \$18.25x = \$161 - \$15x

\$18.25x + \$15x = \$161 - \$28
\$33.25x = \$133

now solve for x:
x = \$133 / \$33.25
x = 4

therefore, your account balances will be the same in week 4.

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