# Question #ccbb7

Oct 26, 2017

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:

$c = 3 + k \text{ }$ (Carlos has $3$ more trolls than Krista)

$a = 4 c \text{ }$ (Amanda has $4$ times as many dolls as Carlos)

$k + c + a = 123 \text{ }$ (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:

$k + \left(3 + k\right) + \left(4 c\right) = 123$

$2 k + 3 + 4 c = 123$

$2 k + 4 c = 120$

$2 k = 120 - 4 c$

$k = 60 - 2 c$

Now that we have $k$, let's plug that back into the first equation:

$c = 3 + \left(60 - 2 c\right)$

$c = 63 - 2 c$

$3 c = 63$

$c = 21$

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 $a$:

$a = 4 \left(21\right)$

$a = 84$

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.