# Question #51f4c

Nov 28, 2017

29

#### Explanation:

Let’s make R stand for the Red marbles, and B for the Black.

From the info given, we can see that red has twice more than black plus 3, so $R = 2 B + 3$

Note that the $T o t a l = R + B$

You want to replace R with the equation we found earlier, so:

$T o t a l = R + B = 2 B + 3 + B$

And since we know the total amount of marbles, we can plug that in.

$42 = 2 B + 3 + B$

Move like terms together (subtract 3 on both sides, 2B+B = 3B)

$39 = 3 B$

Solve B (Divide both sides by 3)

$\frac{39}{3} = \frac{3 B}{3}$

$13 = B$

We have solved the amount of black marbles. There are 13 black marbles!

Now plug it back to the R equation we found earlier to get the amount of red marbles. (Equation is 2B+3.) Since we found the amount of black marbles (B), you can replace B with 13 to find R

$R = 2 B + 3 = 2 \left(13\right) + 3 = 29$

There are therefore 29 red marbles.

Nov 28, 2017

Pam has a total of $29$ red marbles

#### Explanation:

Method 1
Let the number of black marbles be $x$.
Then the number of red marbles is $\left(2 x + 3\right)$

By setting up an equation,
$x + \left(2 x + 3\right) = 42$
$3 x + 3 = 14 \times 3 \text{ } \left(\div 3\right)$
$x + 1 = 14$
$x = 13$

Therefore, Pam has a total of $\left[2 \left(13\right) + 3\right]$
$= 29$ red marbles

Method 2
Let the number of red marbles be $x$.
Then the number of black marbles is $\left(\frac{x - 3}{2}\right)$

By setting up an equation,
$x + \left(\frac{x - 3}{2}\right) = 42 \text{ } \left(\times 2\right)$
$2 x + x - 3 = 84$
$3 x - 3 = 3 \cdot 28 \text{ } \left(\div 3\right)$
$x - 1 = 28$
$x = 29$

Therefore, Pam has a total of $29$ red marbles