Date: 01/22/2001 at 22:49:31 From: Elaien Chesebro Subject: Working Backward This problem was given to my son in 7th grade. He was told to use a working backward strategy to solve it. I cannot figure it out using that method. Can you explain it that way?? Thanks. Ann, Barry, Chip, Doug, Evelyn and Fred went to lunch to celebrate Evelyn's and Fred's birthdays. Each person's meal cost the same amount. Evelyn and Fred were being treated for their meals, but each was to chip in equally for the his or her share of the other's meal. If the bill came to $54.00, HOW MUCH SHOULD EACH PERSON PAY? (Evelyn is being treated, but she is still paying a share of Fred's meal, and the same goes for Fred.) Thanks for any help you can offer.
Date: 01/23/2001 at 08:52:08 From: Doctor Rick Subject: Re: Working Backward Hi, Elaine. Let's see if we can re-state the situation in a way that makes it clearer what is happening. There are 6 people. Evelyn pays nothing for her meal, but the other five share the cost of her meal. That is, each of those five (including Fred) pays for 1/5 of Evelyn's meal. Likewise, Fred does not pay for his meal, but each of the other five (including Evelyn) pays for 1/5 of his meal. The four who are not being treated each pay for their own meal, plus 1/5 of each of Ev's and Fred's meals. We can now make a table showing how many meals each person pays for: Ann 1 2/5 Barry 1 2/5 Chip 1 2/5 Doug 1 2/5 Evelyn 1/5 Fred 1/5 Add up these fractions, and what do we get? Exactly 6. That's no surprise: 6 meals were eaten, and they must all be paid for somehow. This is a check that we've understood the math correctly so far. If we only knew how much one meal cost, we could figure out how much each person paid, couldn't we? We just multiply the cost of a meal by the number of meals. Ann, for instance, paid 1 2/5 times the cost of one meal. Here, at last, is where "working backward" comes in. We know the total cost was $54. We know that there were 6 meals. How much did each meal cost? If we knew the cost per meal, we would multiply it by 6 to get the total cost. Working backward, starting from the total cost, we must DIVIDE by 6 to get the cost per meal: [Cost per meal] * 6 = $54 $54 / 6 = [Cost per meal] We've already figured out how to get from this figure to the amount that each person paid. You can finish the work. - Doctor Rick, The Math Forum http://mathforum.org/dr.math/
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