Zoe has a total of 16 coins. Some of her coins are dimes and some are nickels. The combined value of her nickels and dimes is $1.35. How many nickels and dimes does she have?

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Answer 1 · 2016-11-26T14:38:24

Zoe has 5 nickles and 11 dimes.

First, let's give what we are trying to solve for names. Let's call the number of nickles #n# and the number of dimes #d#.

From the problem we know:

#n + d = 16# She has 16 coins made up of some dimes and some nickles.

#0.05n + 0.1d = 1.35# The value of the dimes with the value of the nickles is $1.35.

Next, we solve the first equation for #d#

#n + d - n = 16 - n#

#d = 16 - n#

Next, we substitute #16 - n# for #d# in the second equation and solve for #n#:

#0.05n + 0.1(16 - n) = 1.35#

#0.05n + 0.1*16 - 0.1n = 1.35#

#(0.05 - 0.1)n + 1.6 = 1.35#

#-0.05n + 1.6 = 1.36#

#-0.05n + 1.6 - 1.6 = 1.35 - 1.6#

#-0.05n = -0.25#

#(-0.05n)/(-0.05) = (-0.25)/(-0.05)#

#n = 5#

Now we can substitute #5# for #n# in the solution for the first equation and calculate #d#:

#d = 16 - 5#

#d = 11#