SOLUTION: Write a system of equations to model each situation. Then use your system to solve. 1) A writing workshop enrolls novelists and poets in a ration of 5 to 3. There are 24 peopl

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Write a system of equations to model each situation. Then use your system to solve. 1) A writing workshop enrolls novelists and poets in a ration of 5 to 3. There are 24 peopl      Log On


   

Question 1033682: Write a system of equations to model each situation. Then use your system to solve.

1) A writing workshop enrolls novelists and poets in a ration of 5 to 3. There are 24 people at the workshop. How many novelists are there? How many poets?
2) You have 15 coins in your pocket that are either quarters or nickels. They total $2.75. How many of each coin do you have?
Found 2 solutions by stanbon, macston:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Write a system of equations to model each situation. Then use your system to solve.
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1) A writing workshop enrolls novelists and poets in a ration of 5 to 3. There are 24 people at the workshop. How many novelists are there? How many poets?
# of novelists = 5x
# of poets = 3x
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Equation:
5x + 3x = 24
8x = 24
x = 3
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# of novelists = 5x = 5*3 = 15
# of poets = 3x = 3*3 = 9
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2) You have 15 coins in your pocket that are either quarters or nickels. They total $2.75. How many of each coin do you have?
Quantity Eq:: n + q = 15 coins
Value Eq:: 5n+25q = 275 cents
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n + q = 15
n + 5q = 55
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Subtract and solve for "q"::
4q = 40
q = 10 (# of quarters)
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n = 15-10 = 5 (# of nickels)
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Cheers,
Stan H.
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Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
According to rules of posting on this web site, you may ask one question per post. I chose to answer your second question:
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2) You have 15 coins in your pocket that are either quarters or nickels. They total $2.75. How many of each coin do you have?
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Q=number of quarters; N=number of nickels
Q+N=15
Q=15-N
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$0.25Q+$0.05N=$2.75
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$0.25(15-N)+$0.05D=$2.75
$3.75-$0.25N+$0.05N=$2.75
-$0.20N=-$1.00
N=5
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ANSWER 1: There are 5 nickels.
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Q=15-N=15-5=10
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ANSWER 2: There are 10 quarters.
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CHECK:
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$0.25Q+$0.05N=$2.75
$0.25(10)+$0.05(5)=$2.75
$2.50+$0.25=$2.75
$2.75=$2.75