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Find how many of each coin is there

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5 Answers

Herbert
 
Let n=the number of nickels and q=the number of quarters.
 
From the problem statement, we know two things:
 
The total number of coins is 57; This means that n+q=57
The total value of the coins is $8.85; Since each nickel is worth .05 and each quarter is worth .25, this means that .05n+.25q=8.85
 
We now have two equations with two unknowns.
 
We can solve for n in the first equation, n=57-q
Plugging this in for n in the second equation, we get .05(57-q)+.25q=8.85
Multiplying through and simplifying:  .05*57-.05q+.25q=8.85
                                                     2.85   +    .20q    =8.85
                                                                     .20q   =8.85-2.85
                                                                     .20q   =6
                                                                         q   = 6/.20
                                                                         q   = 30 (This is the number of quarters)
 
Since n+q=57; n=57-q
                       n=57-30
                       n=27 (this is the number of nickels)
 
We can now double check the results by taking the number of quarters (30) times the value of each quarter (.25) and adding this to the the number of nickels (27) times the value of each nickel (.05):
 
30*.25+27*.05 = 7.50+1.35 = 8.85, which is the value stated in the problem.
 
Let me know if you have any questions.
 
George T.
Let q be the number quarters,n the number of nickles.
q     +n   =  57  ...........................(1)
25q +5n =  885 .....................     .(2)
solve for q &n by either get rid of one of them.Lets omit n by multiply eq 1 by 5
 
5q+5n =  285  (1)'
25q+5n  =885  (2)
subtract (1)' from (2)
20 q = 600
q=30 ,substitute in any eq. n =27
verify your answer:
30 quarter= $7.5
27 nickles= $1.35
Hi Herbert;
x=quantity of nickles
y=quantity of quarters
 
$0.05x+$0.25y=$8.85
 
x+y=57
 
Let's solve for y using the easier equation...
x+y=57
y=57-x
 
Let's proceed with the first equation...
$0.05x+$0.25y=$8.85
Let's cancel the $
0.05x + 0.25y=8.85
Let's plug-in the new equation for y...
0.05x + 0.25(57-x)=8.85
0.05x+14.25-0.25x=8.85
14.25-0.20x=8.85
Let's subtract 14.25 from both sides...
-14.25+14.25-0.20x=8.85-14.25
-0.20x=-5.40
Let's divide both sides by -0.20...
-0.20x/-0.20=-5.40/-0.20
x=27
 
Let's now solve for y...
x+y=57
27+y=57
y=30
 
Let's check our work...
$0.05x+$0.25y=$8.85
$0.05(27) + $0.25(30)=$8.85
$1.35+$7.50=$8.85
$8.85=$8.85
 
There are 27 nickles and 30 quarters in the jar.
Hey Herbert -- try a 30-cent pack ... $9 would have 30Q and 30N => drop 15 cents
by removing 3N ==> 30Q and 27N for 7.50 + 1.00 + 0.35 ... Best wishes, sir :)

Comments

Hi Brad;
Thank you for sharing that information about "pending review".  I was wondering what was going on.  I thought I was being isolated.  Now, I understand Wyzant is probably randomly checking answers.  Which is good!  We cannot be Wyzants without being part of a colony of Wyzants.
Hey VL -- You may thank Robert J. for the "pending review" comment ... I'm unfamiliar with that process.
"Pending review" is likely scanning for phone numbers: (885 minus 285) over 20 will likely get thru o.k.

Comment

Mental math approach: Assume all are nickels. Then there are 57*5 = 285 cents. Since switching one nickel to one quarter increases 20 cents, the number of quarters = (885-285)/20 = 30, and the number of nickels = 57-30 = 27.
 
Check: 30*25 + 27*5 = 885 cents.