A coin collector has $1.70 in dimes and nickels. She has 2 more dimes than nickels. How many nickels does she have?

1 Answer
Aug 9, 2016

10 nickels and 12 dimes

Explanation:

Given that
1 nickel #-> #5 cents
1 dime #-> # 10 cents

100 cents #-># 1 dollar

So 2 nickels is 1 cent

Let the count of nickels be #n#
Let the count of dimes be #d#

Known that $1.70 #-># 1.70xx100 = 170 cents
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So #5n+10d=170#..........................Equation(1)

It is given that there is 2 more dimes than nickels giving:

#d=2+n#...Equation(2)

Using equation(2) substitute for d in equation(1)

#5n+10(2+n)=170#

#5n+10n+20=170#

Subtract 20 from both sides

#15n=150#

Divide both sides by 15

#n=150/15=10#
#color(green)("So there are 10 nickels")#

Thus equation (2) becomes# d=2+n->d=2+10 =12#

#color(green)("So there are 12 dimes")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check #"10 nickels"color(white)(..)-> 10xx5color(white)(.)" cents"=color(white)(.)50" cents"#
#" 12 dimes "color(white)(.)->12xx10" cents"=120" cents"#

#=170" as required"#