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