Let #k# be the number of dolls Krista has.
Let #c# be the number of dolls Carlos has.
Let #a# be the number of dolls Amanda has.
So our three equations would be:
#c = 3 + k" "# (Carlos has #3# more trolls than Krista)
#a = 4c" "# (Amanda has #4# times as many dolls as Carlos)
#k + c + a = 123" "# (the sum of the number of dolls they all have)
So let's plug in the first two equations into the last one, and we get this:
#k + (3 + k) + (4c) = 123#
#2k + 3 + 4c = 123#
#2k + 4c = 120#
#2k = 120 - 4c#
#k = 60 - 2c#
Now that we have #k#, let's plug that back into the first equation:
#c = 3 + (60 - 2c)#
#c = 63 - 2c#
#3c = 63#
#c = 21#
Now that we have the value of #c#, we can plug that into both the first and second equations and find #k# and #a#.
Let's find #k# first:
#21 = 3 + k#
#18 = k#
#k = 18#
Now let's find #a#:
#a = 4(21)#
#a = 84#
In order to check our answers, let's plug the number of dolls for #c#, #k#, and #a# all back into the last equation:
#21 + 18 + 84 = 123#
#123 = 123#
So...
Krista has 18 dolls, Carlos has 21 dolls, and Amanda has 84 dolls.
