# Question #d7550

Apr 11, 2017

See the entire solution process below:

#### Explanation:

First, let's call the number of blue marbles Rosy had first $b$ and the number of white marbles Rosy had first $w$.

$b = 4 w$ - she had 4 times as many blue marbles as white.

$b - 18 = w + 6$ - she gave away 16 blue marbles and got 6 white marbles she had the same number blue and white marbles.

We can substitute $4 w$ from the first equation for $b$ in the second equation and solve for $w$ to find the number of white marbles Rosy had at first:

$b - 18 = w + 6$ becomes:

$4 w - 18 = w + 6$

$4 w - 18 + \textcolor{red}{18} - \textcolor{b l u e}{w} = w + 6 + \textcolor{red}{18} - \textcolor{b l u e}{w}$

$4 w - \textcolor{b l u e}{w} - 18 + \textcolor{red}{18} = w - \textcolor{b l u e}{w} + 6 + \textcolor{red}{18}$

$4 w - 1 \textcolor{b l u e}{w} - 0 = 0 + 24$

$\left(4 - 1\right) \textcolor{b l u e}{w} = 24$

$3 w = 24$

$\frac{3 w}{\textcolor{red}{3}} = \frac{24}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} w}{\cancel{\textcolor{red}{3}}} = 8$

$w = 8$

Now, we can substitute $8$ for $w$ in the first equation to calculate the number of blue marbles Rosy had at first.

$b = 4 w$ becomes:

$b = \left(4 \cdot 8\right)$

$b = 32$

At first Rosy had 32 blue marbles and 8 white marbles.

When she gave away 18 blue marbles away and received 6 more white marbles she had 14 blue marbles and 14 white marbles.