SOLUTION: If I have a total of 30 dimes and quarters and the total value of the coins is $5.70, how many quarters do I have? How many dimes do I have?
I am supposed to solve this using S
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Question 947327: If I have a total of 30 dimes and quarters and the total value of the coins is $5.70, how many quarters do I have? How many dimes do I have?
I am supposed to solve this using Systems of Linear Equations (the elimination method.)
I have written the equations out and know that they should be as follows:
d=dimes and q = quarters
30 = d + q and 5.70 = 0.10d and 0.25q
I've tried 3 different ways of solving it and all have ended up with a different answer that, when tested, proves to be incorrect.
Thanks in advance!
Found 2 solutions by ankor@dixie-net.com, macston:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
If I have a total of 30 dimes and quarters and the total value of the coins is $5.70, how many quarters do I have? How many dimes do I have?
I am supposed to solve this using Systems of Linear Equations (the elimination method.)
I have written the equations out and know that they should be as follows:
d=dimes and q = quarters
30 = d + q and 5.70 = 0.10d and 0.25q
:
lets rewrite the equation that you have:
d + q = 30
.10d + .25q = 5.70
Multiply the 2nd equation by 10, this makes .10 = 1
d + q = 30
d + 2.5q = 57
---------------subtraction eliminates d, find q
0 - 1.5q = -27
q = -27/-1.5
q = 18 quarters
find d using the 1st equation
d + 18 = 30
d = 12 dimes
:
:
Check solution in the 2nd original equation
.10(12) + .25(18) =
1.20 + 4.50 = 5.70
:
Did this help?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
d=dimes; q=quarters
d+q=30 solve for d, subtract q from each side
d=30-q
$0.10d+$0.25q=$5.70
METHOD 1:
Substitute for d
$0.10(30-q)+$0.25q=$5.70
$3.00-$0.10q+$0.25q=$5.70 Subtract $3.00 from each side
$0.15q=$2.70 Divide each side by $0.15
q=18 ANSWER 1 There are 18 quarters.
d=30-q=30-18=12 ANSWER 2 There are 12 dimes.
CHECK
$0.10(12)+$0.25(18)=$5.70
$1.20+$4.50=$5.70
$5.70=$5.70
METHOD 2:
d+q=30 Multiply this by $0.10 and subtract from equation below
$0.10d+$0.25q=$5.70
$0.10d+$0.10q=$3.00
____________________
$0.15q=$2.70
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