Question 886852: Maria has some nickels, dimes, and quarters. She has three more nickels than twice the number of dimes, and twice as many quarters as dimes. If the total value of her money is $14.85, how many of each kind of coin does Maria have?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39621)   (Show Source):
You can put this solution on YOUR website! Equations from the description:  ;  ;  .
Arrange into a simplified system in n, d, q, constant.
n-2d=3; q=2d, -2d+q=0, 2d-q=0, ; 5n+10d+25q=1485, n+2d+5q=297.
SYSTEM:
----------------
n+2d+5q=297
'
n-2d=3
'
2d-q=0
----------------
Variety of ways to go but basically the methods are Substitution, Elimination, or Matrix row operations.
If you know enough about handling as a matrix, then you could start with this:
ADDED July 12----
Solving again to do it correctly:
-------------------------
System of Equations:
------------------------
Substitute for q.
--------------------
--------------------
-----------------
----------------
SUBTRACT the "3" equation from the "297" equation.
 , answer for one of the coins, the dimes.
Returning to , find  ,  , answer for quarters.
Using n-2d=3
 , for how many nickels.
--
Note that my method done separately on paper was to solve the last equation for q, and substitute this into the other two equations. Simplifying and using elimination method gave d=21.071429 something... Not a whole number. Whole numbers are expected for such coin-problems.
-
...
SUMMARY:
n=45
d=21
q=42
CHECK? 0.05*45+0.10*21+0.25*42=14.85,
CHECKS perfectly.
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website! Maria has some nickels, dimes, and quarters. She has three more nickels than twice the number of dimes, and twice as many quarters as dimes. If the total value of her money is $14.85, how many of each kind of coin does Maria have?
Let number of dimes be D
Then number of nickels is: 2D + 3
Number of quarters is: 2D
We now have: .1D + .05(2D + 3) + .25(2D) = 14.85
.1D + .1D + .15 + .5D = 14.85
.7D = 14.85 - .15
.7D = 14.7
D, or number of dimes =  , or 
You should be able to find the number of nickels, and number of quarters.
Do a check after!!
If you need a complete and detailed solution, let me know!!
Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
Further help is available, online or in-person, for a fee, obviously.
For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL
MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra,
Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE,
GRE, CLEP, and the TASC/GED, you can visit: http://asvabstudyzone.freeforums.net/.
|
|
|
