SOLUTION: Translate the problem into a pair of linear equations in two variables. Solve using elimination or substitution. Joe has a collection of nickels and dimes that is worth $5.65 .

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Question 266930: Translate the problem into a pair of linear equations in two variables. Solve using elimination or substitution.
Joe has a collection of nickels and dimes that is worth $5.65 . If the number of dimes was doubled and the number of nickels was increased by 2, then the value of the coins would be $10.15 . How many dimes does he have?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
take it sentence by sentence
"Joe has a collection of nickels and dimes that is worth $5.65 "
this means: N%2BD=5.65


"If the number of dimes was doubled and the number of nickels was increased by 2, then the value of the coins would be $10.15"
this means: 2D%2B%28N%2B.10%29=10.15 (2nickels=$.10)


I would use Substitution method
N%2BD=5.65
D=5.65-N
Plug D in to other equation
2D%2B%28N%2B.10%29=10.15
2%285.65-N%29%2B%28N%2B10%29=10.15
11.3-2N%2BN%2B.10=10.15
11.4-N-11.4=10.15-11.4
-N=-1.25
N=1.25 this equals value of the nickels, divide by .05 for answer
25 nickels
_______________________
Plug N=1.25 into 1st equation
N%2BD=5.65
1.25%2BD=5.65
1.25%2BD-1.25=5.65-1.25
D=4.4 this equals value of the dimes divide by .10 for answer
44 dimes