SOLUTION: You have a total of 21 coins that are nickels and quarters. The coins have a value of 2.25$. how many quarters do you have ? please explain work.

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Question 1000026: You have a total of 21 coins that are nickels and quarters. The coins have a value of 2.25$. how many quarters do you have ?
please explain work.
Found 2 solutions by macston, Fiona26295:
Answer by macston(5194) (Show Source):
You can put this solution on YOUR website!
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N=number of nickels; Q=number of quarters
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N+Q=21
Q=21-N . Use this to substitute for Q below.
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$0.05N+$0.25Q=$2.25 . This converts number of coins to value.
$0.05N+$0.25(21-N)=$2.25 . This substitutes for Q from above.
$0.05N+$5.25-$0.25N=$2.25
-$0.20N=-$3.00
N=15
You have 15 nickels.
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Q=21-N=21-15=6
ANSWER: You have 6 quarters
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CHECK:
$0.05N+$0.25Q=$2.25
$0.05(15)+$0.25(6)=$2.25
$0.75+$1.50=$2.25
$2.25=$2.25

Answer by Fiona26295(4) (Show Source):
You can put this solution on YOUR website!
This is a system of equations
n=nickels
q= quarters
You have a total of 21 coins so your first equation is n+q=21
Nickels are each worth .05 cents and quarters are equal to .25 cents so your second equation is .05n+.25q=2.25
Eliminate one of your variables by multiplying the entire first equation by -.05
-.05n-.05q=-1.05
Add this equation to .05n+.25q=2.25 in order to eliminate your n variable
.2q=1.2
Divide and solve
q=6
You have 6 quarters