Finding Sally's Hourly WageDate: Mon, 7 Nov 1994 17:37:53 -0500 From: Rich Joseph Subject: Ashley Petrylak Dear Dr. Math, My name is Ashley Petrylak and I'm In the MathCounts program at E.T.Richardson Middle School.I need to do two worksheets for homework. I am having trouble with the following problems. Sally works at a grocery store. In one week she earned $390 for working 47 hours, of which 7 hours were overtime.The next week she earned $416 for working 50 hours, of which 8 hours were overtime. What is Sally's hourly rate? Here's what I've already tried: 40r + (7r + 7o) = $390 47r + 7o = $390 42r + (8r + 8o) = $416 50r + 8o = $416 When I tried to get r by itself, I had trouble because I couldn't make sense of the division, 47r + 7o ________ 47 Please help! Date: Mon, 7 Nov 1994 18:22:56 -0500 (EST) From: "Michael W. S. Morton" Subject: Re: Ashley Petrylak Great Problem! The first thing I did when I looked at the problem is the same thing you did, only a little different. Let's define Sally's hourly rate and her overtime rate. Say, Sally's hourly rate = r Sally's overtime rate = o Then we get the two equations: 40r + 7o = $390 since the first 40 hours were normal pay, and the next 7 hours were overtime pay. 42r + 8o = $416 again, the first 42 hours were normal pay, the next 8 overtime. So, we need to solve for r which is possible because we have two equations and two unknowns (r and o). Let's try multiplying the first equation by 8 and the second equation by -7. 8 * (40r + 7o = $390) => 320r + 56o = $3120 -7 * (42r + 8o = $416) => -294r - 56o = -$2912 Then, let's add the two equations above together: 320r + 56o = $3120 -294r - 56o = -$2912 -------------------- 26r + 0o = $ 208 Now we have one equation and only one unknown! See if you can solve that, and then you could even find Sally's overtime pay by substituting that value back into one of the other earlier equations! Hope all that makes sense.... write us back if it doesn't! -MORTON, Doctor on call. X-Mailer: Eudora 1.3.1+Swarthmore Date: Mon, 7 Nov 1994 18:30:06 +0900 Subject: Re: Ashley Petrylak Hi Ashley- Thanks for writing to us. I did MathCounts when I was in 7th and 8th grade myself. So I am very excited to hear from you. You have set up the problem perfectly. In order to isolate the r, you need to subtract the 7o from both sides first and then divide by 47. So you get: 47r + 7o = $390 is the same as 47r = 390 - 7o which is the same as 390 - 7o r = -------- 47 Then take this value for r and plug it into your second equation (50r+8o=516) Then you will have all o's, so solve for o and your almost there. I hope this helps. Please write back if its not clear or if you have any other questions. -Margaret, a Math Doctor |
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