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May 10th, 2008, 02:05 PM  #1 
Newbie Joined: May 2008 Posts: 1 Thanks: 0  A problem that has me rather stumped.
Phil T. Rich has $100 and spends $3.00 of it per day. Ernest Worker has only $20 but is adding to it at a rate of $5.00 per day. Let x be the number of days that have passed. Write the definition of x. Then write two expressions, one representing how much Phil has after x days and the other representing how much Ernest has after x days. Who has more money , and how much more, after: i. 1 week ii. 2 weeks After how many days will each have the same amount of money? Write and solve an equation to find this number of days. Show that each actually does have the same amount of money after the number of days you calculated in part c. (Work required) I've been looking at this one since yesterday. I am not inclined for mathematics, so this is kind of like trying to read another language. Any help would be GREATLY appreciated. 
May 10th, 2008, 03:13 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,281 Thanks: 1965 
Well, x will be the number of days that have passed (since the day when Phil T. Rich has $100). This will apply until x = 33 1/3, since Phil T. Rich can't spend money he doesn't have. After x days, Phil has (100  3x) dollars and Ernest has (20 + 5x) dollars. After 1 week (i.e., 7 days), Phil has $79 and Ernest has $55, so Phil has $24 more than Ernest. After 2 weeks (i.e., 14 days), Phil has $58 and Ernest has $90, so Ernest has $32 more than Phil. After 10 days, each has $70 (since 100  3x = 20 + 5x implies 100  20 = 5x + 3x, i.e., 100 = 8x, i.e., x = 10). Confirmation: $(100  (3 × 10)) = $70 and $(20 + (5 × 10)) = $70. 

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