SOLUTION: A jar contains quarters and nickels. There are 25 coins in the jar, and the total value of the coins is $5.05 How many quarters and how many nickels are in the jar?

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Coins -> SOLUTION: A jar contains quarters and nickels. There are 25 coins in the jar, and the total value of the coins is $5.05 How many quarters and how many nickels are in the jar?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 189846: A jar contains quarters and nickels. There are 25 coins in the jar, and the total value of the coins is $5.05
How many quarters and how many nickels are in the jar?
Found 3 solutions by Edwin McCravy, vannac, greta_elisif:
Answer by Edwin McCravy(8908) About Me  (Show Source):
You can put this solution on YOUR website!
A jar contains quarters and nickels. There are 25 coins in the jar, and the total value of the coins is $5.05
How many quarters and how many nickels are in the jar?
>>...A jar contains quarters and nickels. There are 25
coins in the jar...<<

Translation:

(NUMBER OF QUARTERS) 

plus 

(NUMBER OF NICKELS)

equals

25

or   N + Q = 25

>>...the total value of the coins is $5.05...<<

Translation:

(5 cents times the NUMBER OF NICKELS) 

plus 

(25 cents times the NUMBER OF QUARTERS) 

equals

505 cents 

or  5N + 25Q = 505

Can you solve this system?  

system%28N%2BQ=25%2C+5N%2B25Q=505%29

If not post again asking how to.

Answer: 6 NICKELS and 19 QUARTERS.

Edwin


Answer by vannac(1) About Me  (Show Source):
You can put this solution on YOUR website!
19quarters = $4.75, 6 nickels=0.30, $4.75+0.30=$ 5.05
There are 19 quarters, and 6 nickels.

Answer by greta_elisif(10) About Me  (Show Source):
You can put this solution on YOUR website!
A jar contains quarters and nickels. There are 25 coins in the jar, and the total value of the coins is $5.05
How many quarters and how many nickels are in the jar?
1. Define the variables:
q = number of quarters
n = number of nickels
❧
3. Define two more values:
.25q = value of the quarters, in dollars
.05n = value of the nickels, in dollars
❧
3. Since the number of quarters plus the number of nickels equals 25, set up this equation to solve:
q+%2B+n+=+25
❧
4. Solve for one variable by subtracting the other from both sides:
q+%2B+n+-+n+=+25+-+n
q+=+25+-+n
❧
5. Since the value of the quarters plus the value of the nickels equals $5.05, set up this equation next:
.25q+%2B+.05n+=+5.05
❧
6. Replace q with what it equals:
.25%2825+-+n%29+%2B+.05n+=+5.05
❧
7. Distribute .25:
6.25+-+.25n+%2B+.05n+=+5.05
❧
8. Simplify the variable terms:
6.25+-+.2n+=+5.05
❧
9. Subtract 6.25 from both sides:
6.25+-+.2n+-+6.25+=+5.05+-+6.25
-.2n+=+-1.2
❧
10. Divide both sides by -.2:
%28-.2n%29%2F-.2+=+%28-1.2%29%2F-.2
n+=+6
❧
11. With n found, q can be found by replacing it in q+=+25+-+n with what it equals:
q+=+25+-+6
❧
12. Subtract and get:
q+=+19
❧
13. Combine the answers with the definitions of the variables to write the answer:
“There are 19 quarters and 6 nickels in the jar.”
❧
14. To check:
Add 19 and 6, getting 25.
and
Multiply the value of a quarter times 19, getting $4.75, and the value of a nickel times 6, getting $.30, and add the amounts of money, getting $5.05.