Girls and CoinsDate: 01/29/2001 at 21:17:25 From: shana Subject: Coin combinations Five girls stopped for a soda on the way home from school. The girls were amazed to find that each of them had exactly six coins. Each of them had at least one of four types of coins (penny, nickel, dime, and quarter). 1. Betty had one more nickel than Alice, but Alice had 5 cents more in all than Betty. 2. Donna had one more nickel than Betty, but Betty had 5 cents more in all than Donna. 3. Eve had one more nickel than Carol, but Carol had 5 cents more in all than Eve. 4. Carol had one more penny than Donna, she had 1 cent more than Donna, and she also had 1 cent more in all than Donna. How much money did each girl have? Make a chart of the possible combinations. Date: 01/30/2001 at 13:11:34 From: Doctor Keith Subject: Re: Coin combinations Hi Shana, When you have a problem like this, with lots of information, a chart is the only way to go. Luckily our chart does not have to include four of the six coins because we already know what they are. We only need to worry about the two we don't know. Let's make a chart: | Coin 1 | Coin 2 | Notes ------+--------+--------+------- Alice | | | ------+--------+--------+------- Betty | | | ------+--------+--------+------- Carol | | | ------+--------+--------+------- Donna | | | ------+--------+--------+------- Eve | | | Now we have to go through the clues step by step. We will start with clue 1. > 1. Betty had one more nickel than Alice, but Alice had 5 cents more in all than Betty. We can tell that Betty has at least one nickle (she may have more but she at least has one). We also see that Alice has 5 cents more than Betty, so we hold onto this information for later. We can mark this in our chart: | Coin 1 | Coin 2 | Notes ------+--------+--------+------- Alice | | | 5 cents more than Betty ------+--------+--------+------- Betty | Nickle | | ------+--------+--------+------- Carol | | | ------+--------+--------+------- Donna | | | ------+--------+--------+------- Eve | | | We now move on to hint 2: > 2. Donna had one more nickel than Betty, but Betty had 5 cents more in all than Donna. This one gives us a lot of information. For Donna to have a nickle more than Betty, Donna must have two and Betty must have one. Donna has a total of 10 centsand Betty has 5 cents more, so Betty has 15 cents. Thus Betty must have a dime also, since there is no other coin you can add to a nickle to get 15 cents. | Coin 1 | Coin 2 | Notes ------+--------+--------+------- Alice | | | 5 cents more than Betty ------+--------+--------+------- Betty | Nickle | Dime | ------+--------+--------+------- Carol | | | ------+--------+--------+------- Donna | Nickle | Nickle | ------+--------+--------+------- Eve | | | At this point I am going to leave filling the chart in to you. I will ask you some questions to think about which should lead you to the answer. Now that we know how much Betty has, can you tell me how much Alice has? To get that amount what are the only two coins she could have? Now look at hint 3: > 3. Eve had one more nickel than Carol, but Carol had 5 cents more in all than Eve. and compare with hint 1: > 1. Betty had one more nickel than Alice, but Alice had 5 cents more in all than Betty. How are these similar? How should you fill in the chart? Finally you need to look at hint 4: > 4. Carol had one more penny than Donna, she had 1 cent more than Donna, and she also had 1 cent more in all than Donna. What is the total of Donna's two coins? Since Carol has 1 cent more, how much does Carol have? What must the coins be that Carol has to total this? Now that you have Carol's total, you can go back to hint 3 and find out what Eve has, since Carol has 5 cents more than Eve. Thanks for writing in. If you have any questions on what we did or other problems in the future, write back and we will be glad to help. Best wishes, - Doctor Keith, The Math Forum http://mathforum.org/dr.math/ |
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