[WORD PROBLEM] How many of each kind of coin are there?

[arcticaction]

Question: A collection of nickels, dimes, and quarters total $6.00. If there are 52 coins altogether and twice as many dimes as nickels, how many of each kind of coin are there?' I don't understand how to write out the equation so i can solve it by using a system of equations.

 

[wjm11]

Question: A collection of nickels, dimes, and quarters total $6.00. If there are 52 coins altogether and twice as many dimes as nickels, how many of each kind of coin are there?' I don't understand how to write out the equation so i can solve it by using a system of equations.

Here are some examples to study. After you have reviewed them, try to come up with equations for your problem.

http://www.algebra.com/algebra/homework/word/coins/Word_Problems_With_Coins.faq.question.171118.html

http://www.purplemath.com/modules/coinprob.htm

http://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.300978.html

 

[arcticaction]

Here are some examples to study. After you have reviewed them, try to come up with equations for your problem.

http://www.algebra.com/algebra/homework/word/coins/Word_Problems_With_Coins.faq.question.171118.html

http://www.purplemath.com/modules/coinprob.htm

http://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.300978.html

I have reviewed the examples and came up with this equation. X= # of nickels 5x+10y+25z=600 (Dealing in pennies)
---------------------------------------------------------------------------Y= # of dimes --------x+y+z=52
---------------------------------------------------------------------------Z= # of quarters -----------x=2y

 

[DrPhil]

Question: A collection of nickels, dimes, and quarters total $6.00. If there are 52 coins altogether and twice as many dimes as nickels, how many of each kind of coin are there?' I don't understand how to write out the equation so i can solve it by using a system of equations.

When translating from English to Algebra, the first thing I do is read through looking for the question mark. I find it here with the phrase
how many of each kind of coin are there?
Going back to the beginning again, I find the phrase
A collection of nickels, dimes, and quarters
That translates to three unknowns, so I begin the algebraic statements with
.....Let N = number of nickles
.. ........D = number of dimes
... .......Q = number of quarters

Since there are three unknowns, I know I have to extract three equations from the English text.
total $6.00
becomes
.........0.05 N + 0.10 D + 0.25 Q = 6.00
there are 52 coins altogether
becomes
.................N +.........D + ....... Q = 52
twice as many dimes as nickels
becomes D=2N, or
..............2 N \(\displaystyle -\) .......D.................= 0