Jocelyn has $1.95 in her pocket made up of 27 nickels and dimes. How many of each type of coin does she have?

Question

Genesis Allen · Accepted Answer

Jocelyn has 15 nickels and 12 dimes in her pocket.

First, let's call the number of dimes Jocelyn has #d# and the number of nickels she has #n#. We then know the number of dimes and the number of nickels are 27 or #d + n = 27# We can solve this for #d#: #d + n - n = 27 - n# #d = 27 - n# Next we know a dime is worth #$0.10# and a nickel is worth #$0.05# and we know she has a total of #$1.95# in her pocket so we can write: #$0.10d + $0.05n = $1.95# From the first equation we can substitute #27 - n# for #d# in the second equation and solve for #n#; #$0.10(27 - n) + $0.05n = $1.95# #($0.10*27) - $0.10n + $0.05n = $1.95# #$2.70 - $0.05n = $1.95# #$2.70 - $2.70 - $0.05n = $1.95 - $2.70# #-$0.05n = -$0.75# #(-$0.05n)/(-$0.05) = (-$0.75)/(-$0.05)# #n = 15# Now that we know there are 15 nickels (#n = 15#) we can substitute #15# for #n# in the solution for the first equation and calculate the number of dimes or #d#: #d = 27 - 15# #d = 12#

Nathan Axel · Answer

undefined Jocelyn has 21 nickels and 6 dimes.