Question #ccbb7

1 Answer
Oct 26, 2017

Answer:

Krista has 18 dolls, Carlos has 21 dolls, and Amanda has 84 dolls.

Explanation:

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.