Question 266930
take it sentence by sentence
"Joe has a collection of nickels and dimes that is worth $5.65 "
this means: {{{N+D=5.65}}}
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"If the number of dimes was doubled and the number of nickels was increased by 2, then the value of the coins would be $10.15"
this means: {{{2D+(N+.10)=10.15}}} (2nickels=$.10)
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I would use Substitution method
{{{N+D=5.65}}}
{{{D=5.65-N}}}
Plug D in to other equation 
{{{2D+(N+.10)=10.15}}}
{{{2(5.65-N)+(N+10)=10.15}}}
{{{11.3-2N+N+.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
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Plug N=1.25 into 1st equation
{{{N+D=5.65}}}
{{{1.25+D=5.65}}}
{{{1.25+D-1.25=5.65-1.25}}}
{{{D=4.4}}} this equals value of the dimes divide by .10 for answer
44 dimes