Number of Quarters
Date: 9/11/96 at 19:32:28 From: Michael F. Biondi Subject: Number of Quarters Dear Dr. Math, How do I write an algebraic equation for the following problem? Tony has eleven more nickels than quarters. How many quarters does he have if the total value of his coins is $2.65? I am stumped on this question. Thanks for any help you can give me. Eliza
Date: 9/12/96 at 14:4:27 From: Doctor Mike Subject: Re: Number of Quarters Hi Eliza, Letting q be the number of quarters is a good start. The total amount of money for q quarters is 25*q cents. The problem says that he also has q+11 nickels. The total amount of money for q+11 nickels is 5*(q+11) cents. Now the other fact in the problem is that the total money (from the value of the quarters and from the value of the nickels all together) is 265 cents. So, one way to write the equation would be: "money for q quarters" + "money for q+11 nickels" = 265 Now rewrite this using just algebra expressions without words and you have it. If there is still something you don't understand just write back. (By the way, the reason I used cents instead of dollars was to avoid working with decimals. Whole numbers representing cents are easier to work with I think. I also use cents when I balance my checking account register each month for the same reason.) I hope this helps. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/
Date: 9/12/96 at 10:35:43 From: Doctor Robert Subject: Re: Number of Quarters If Tony has Q quarters as you say, then he must have Q+11 nickels because the problem says so. Now, what is the value of his coins. Each quarter is worth $.25. Since he has Q quarters he must have (.25)Q dollars in quarters. Since each nickel is worth $.05, he must have (Q+11)(.05) dollars in nickels. The total amount that he has is the sum of these two and is equal to $2.65. So the equation becomes .25Q + .05(Q+11) = 2.65 .3Q + .55 = 2.65 .3Q = 2.10 Q = 7 Tony has 7 quarters and 18 nickels. Does it check? 7 quarters is worth $1.75 and 18 nickels is worth $.90. They add up to $2.65! -Doctor Robert, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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