Question

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?

Answer 1

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 = mx+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=5x+40`

Susan's equation is

`y=-5x+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

`5x+40=-5x+90`

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

`10x+40=90`

Subtract `40` from both sides of this equation.

`10x=50`

Divide both sides of this equation by `10`.

`x=5` weeks