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?

1 Answer
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 = 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