SOLUTION: Natalie has some nickles, Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters, If Natalie gives Dirk a nickle, Dirk gives Quincy

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Question 215046This question is from textbook Algebra Structure and Method, Book 1
: Natalie has some nickles, Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters, If Natalie gives Dirk a nickle, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter, they will all have the same amount of money. How many coins did they each have originally? This question is from textbook Algebra Structure and Method, Book 1

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
Natalie has some nickles, Dirk has some dimes, and Quincy has some quarters. Dirk has five more dimes than Quincy has quarters, If Natalie gives Dirk a nickle, Dirk gives Quincy a dime, and Quincy gives Natalie a quarter, they will all have the same amount of money. How many coins did they each have originally?

Step 1. Let x be the number of nickles, let y be the number of dimes and let z be the number of quarters.
Step 2. y=5+z Equation A
Step 2. Let .05x be the original amount of Natalie, .10y be the original amount of Dirk, and 0.25z be the original amount of Quincy.

Step 3. .05(x-1)+.25=.10(y-1)+.05 =0.25(z-1)+0.10 based on the problem statement where they have the same amount of money after exchanging coins

.05x%2B.20=.10y-.05=.25z-.15

.05x%2B.20=.10y-.05

.05x=.10%28y-1%29-.25 Equation B

.05x%2B.20=.25z-.15

.05x-.25z=-0.35 Equation C

.10y-.05=.25z-.15

.10y=.25z-.10 Equation D




Now we have a system of equations given as Equation A and D in terms of x and y
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving -1*z to the right, we get:
1%2Ay+=+5+-+-1%2Az, or y+=+5%2F1+-+-1%2Az%2F1. Substitute that
into another equation:
0.1%2A%285%2F1+-+-1%2Az%2F1%29+%2B+-0.25%5Cz+=+-0.1 and simplify: So, we know that z=4. Since y+=+5%2F1+-+-1%2Az%2F1, y=9.

Answer: system%28+y=9%2C+z=4+%29.



Given y=9, z=4 then

.05x=.10%28y-1%29-.25

.05x=.10%2A8-.25

.05x=.80-.25=.65

x=13

ANSWER. Natalie has 13 nickels, Dirk has 9 dimes, and Quincy has 4 quarters

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J