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?

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(20056)   (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? If not post again asking how to. Answer: 6 NICKELS and 19 QUARTERS. Edwin

Answer by vannac(1)   (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)   (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:
= value of the quarters, in dollars
= value of the nickels, in dollars
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3. Since the number of quarters plus the number of nickels equals 25, set up this equation to solve:

❧
4. Solve for one variable by subtracting the other from both sides:

❧
5. Since the value of the quarters plus the value of the nickels equals $5.05, set up this equation next:

❧
6. Replace q with what it equals:

❧
7. Distribute .25:

❧
8. Simplify the variable terms:

❧
9. Subtract 6.25 from both sides:

❧
10. Divide both sides by -.2:

❧
11. With n found, q can be found by replacing it in with what it equals:

❧
12. Subtract and get:

❧
13. Combine the answers with the definitions of the variables to write the answer:
“There are 19 quarters and 6 nickels in the jar.”
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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.
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