The total value of a collection of quarters and nickels is $3.75. If the total number of coins is 27, how many of each type of coin are there?

Question

The total value of a collection of quarters and nickels is $3.75.   If the total number of coins is 27, how many of each type of coin are there?

anonymous · Answer

@ganeshie8

anonymous · Answer

@Hero

hero · Answer

let:
n = nickels
q = quarters, 

then:
n + q = 27
.05n + .25q = 3.75

Solve the system

anonymous · Answer

75 nickels

anonymous · Answer

@Hero

hero · Answer

There's only 27 coins in total. So there can't be 75 nickels. Do you know how to solve systems of equations?

anonymous · Answer

nope

hero · Answer

This video should help: https://www.youtube.com/watch?v=nok99JOhcjo

anonymous · Answer

3.75 - .25=3.50

imstuck · Answer

Are you still having trouble with this?

anonymous · Answer

yea

hero · Answer

@alyygirl, the goal is to solve for variables n and d.

imstuck · Answer

Ok, first relate the NUMBER of coins in one equation, and then in the second equation, deal with the VALUE of the coins.  You have nickels, n, and quarters, q, and there is a total number of 27 of them, so the first equation is: 
q + n = 27.

anonymous · Answer

well the answer would help since solving it makes no sense

imstuck · Answer

The second equation will relate the value of the coins to the total value you're given which is 3.75.  The difficult thing to do here is to remember that since a quarter is worth .25, then the value of the number of quarters you have, q, is .25q.  Do the same with the nickels.  The number of nickels you have, n, translates to .05n, because each nickel you have, even though you don't know the number of nickels, is worth 5 cents.  This value of quarters, .25q, addded to the value of nickels, .05n equals 3.75.  So the second equation is .25q + .05n = 3.75.  Both equations look like this now:

imstuck · Answer

q  +   n   =   27
.25q + .05n = 3.75

imstuck · Answer

Do you know how to solve a system of equations?

anonymous · Answer

im stuck from there actually

imstuck · Answer

Hint:  solve the first equation for q.  Like this...  q =

anonymous · Answer

how would I get q?

hero · Answer

Start with the equation
q + n = 27

Then subtract n from both sides.

imstuck · Answer

Subtract n from both sides, like this:
q + n - n = 27 - n
On the left side, a +n and a -n cancel each other out.  So what does q=   ?

imstuck · Answer

Youre not solving for a value for q when we ask you to solve that equation for q, we mean to put the equation in terms of q.  That means, "q = "  That's in terms of q.

anonymous · Answer

there is no a

imstuck · Answer

No a, that was meant as  a  "+n" and a "-n".  +n -n = 0.  N's are gone.

anonymous · Answer

23.25

imstuck · Answer

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