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Answer 1 · 2017-10-26T04:53:59

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

Let $k$ $k$ be the number of dolls Krista has.
Let $c$ $c$ be the number of dolls Carlos has.
Let $a$ $a$ be the number of dolls Amanda has.

So our three equations would be:

$c = 3 + k$ $c = 3 + k" "$ (Carlos has $3$ $3$ more trolls than Krista)

$a = 4 c$ $a = 4c" "$ (Amanda has $4$ $4$ times as many dolls as Carlos)

$k + c + a = 123$ $k + c + a = 123" "$ (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:

$k + (3 + k) + (4 c) = 123$ $k + (3 + k) + (4c) = 123$

$2 k + 3 + 4 c = 123$ $2k + 3 + 4c = 123$

$2 k + 4 c = 120$ $2k + 4c = 120$

$2 k = 120 - 4 c$ $2k = 120 - 4c$

$k = 60 - 2 c$ $k = 60 - 2c$

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

$c = 3 + (60 - 2 c)$ $c = 3 + (60 - 2c)$

$c = 63 - 2 c$ $c = 63 - 2c$

$3 c = 63$ $3c = 63$

$c = 21$ $c = 21$

Now that we have the value of $c$ $c$ , we can plug that into both the first and second equations and find $k$ $k$ and $a$ $a$ .

Let's find $k$ $k$ first:

$21 = 3 + k$ $21 = 3 + k$

$18 = k$ $18 = k$

$k = 18$ $k = 18$

Now let's find $a$ $a$ :

$a = 4 (21)$ $a = 4(21)$

$a = 84$ $a = 84$

In order to check our answers, let's plug the number of dolls for $c$ $c$ , $k$ $k$ , and $a$ $a$ all back into the last equation:

$21 + 18 + 84 = 123$ $21 + 18 + 84 = 123$

$123 = 123$ $123 = 123$

So...

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