Algebra: Structure And Method, Book 1

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Question

Chapter 3.7, Problem 18P

To determine

To determine the number of coins of each person.

Expert Solution & Answer

Answer to Problem 18P

Natalie had 13 nickels

Dirk had 9 dimes

Quincy had 4 quarters

Explanation of Solution

Given:

Natalie has some nickels; Dirk has some dimes and Quincy has some quarters.

Dirk has five more dimes than Quincy has quarters.

If Natalie gives Dirk a nickel, Dirk gives Quincy a dime and Quincy gives Natalie a quarter, they will have the same amount of money.

Calculation:

Let,

Quincy has x quarters.

Then, Dirk has (x+5) dimes.

And let, Natalie has y nickels.

If Natalie gives Dirk a nickel, Dirk gives Quincy a dime and Quincy gives Natalie a quarter, they will have the same amount of money.

So, after giveaway,

Quincy has x - 1 quarters and 1 dime; These worth [10+25(x−1)] cents.

Dirk has 1 nickel and (x+4) dimes; These worth [5+10(x+4)] cents.

Natalie has nickels and 1 quarters; These worth [25+5(y−1)] cents.

According to the problem,

10+25(x−1)=5+10(x+4)=25+5(y−1)

Taking first two parts:

⇒10+25(x−1)=5+10(x+4)⇒10+25x−25=5+10x+40⇒25x−10x=45+15⇒15x=60⇒x=4

Now taking the last two parts:

⇒5+10(x+4)=25+5(y−1)⇒5+10(4+4)=25+5y−5⇒5+80=20+5y⇒5y=85−20⇒5y=65⇒y=13

Conclusion:

Therefore, Natalie had 13 nickels, Dirk had 9 dimes and Quincy had 4 quarters.

Chapter 3.7, Problem 17P

Chapter 3.7, Problem 1MRE

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

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