25 Coins for a DollarDate: 02/13/2003 at 20:02:48 From: Melissa Subject: Math I need 25 coins for my dollar. What are they? Date: 02/14/2003 at 02:40:45 From: Doctor Jeremiah Subject: Re: Math Hi Melissa, Lets use d for dimes, n for nickels and p for pennies. The total number of coins is d + n + p (which equals 25) so one of the equations is d + n + p = 25. The total number of cents of all the dimes is 10d and the total number of cents of all the nickels is 5n, and since pennies are worth one cent the total number of cents of all the pennies is just p. The total number of cents of all the coins put together is 10d + 5n + p (and all the coins add up to 100 cents) so the other equation is 10d + 5n + p = 100 Now if we can solve these equations we will get somewhere. We can combine the equations to remove p. When we do that we get: 10d + 5n + p = 100 d + n + p = 25 ================== 9d + 4n = 75 Let's isolate one of the variables - say d for example: d + 4n/9 = 75/9 The left has two things added together, so we should change the right side so that we have two things added together. d + 4n/9 = 7 + 12/9 Notice how the left side and the right side match up really nicely? If we make d equal 7, then 4n will equal 12 when n equals 3. So d=7 and n=3. But that doesn't make 25 coins. Remember that there were pennies too? If we stick d=7 and n=3 into this equation: d + n + p = 25 7 + 3 + p = 25 p = 15 Now let's check our answer by sticking d=7 and n=3 in this equation: 10d + 5n + p = 100 70 + 15 + p = 100 p = 15 So our answers are right. But they are not the only answer. If you use quarters also, you can do it the same way and get d=3 q=1 n=6 p=15. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/ |
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