Sam was given $40.00 for his birthday and saves$5.00 of his allowance each week, while Susan has $90.00 but spends her weekly allowance plus$5.00 of her savings each week. When will they have the same amount?

Apr 17, 2018

Sam and Susan will have the same amount of money in 5 weeks.

Explanation:

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For both people, their bank account changes linearly. The general functional form for this is

$y = m x + b$.

You've probably seen this equation before, but HERE, because this is a word problem, $y$, $x$, $m$ and $b$ have very specific meanings.

$y$ = the total amount of money in a person's bank account.

$x$ = the number of weeks that pass after their initial deposit.

$m$ = the net amount of money the person saves or spends in one week. If the person has a net saving, $m$ is positive. If the person has a net spending $m$ is negative.

$b$ = the amount of the initial deposit.

Sam's equation is

$y = 5 x + 40$

Susan's equation is

$y = - 5 x + 90$

The question is when do they have the same amount of money? That is, when are these two $y$'s described by these two equations the same? Mathematically, they are asking you to find the value of $x$ when

$5 x + 40 = - 5 x + 90$

Add $5 x$ to both sides of this equation.

$10 x + 40 = 90$

Subtract $40$ from both sides of this equation.

$10 x = 50$

Divide both sides of this equation by $10$.

$x = 5$ weeks