Question

Drew has 50 red, green, and blue marbles. He has six more red marbles than blue marbles and four fewer green marbles than blue marbles. Write and solve an equation to determine how many blue marbles Drew has.

Answer 1

Let \(x\) be the number of red marbles, \(y\) the number of green marbles, and \(z\) the number of blue marbles.

You're given 6 more red marbles than blue, or \(x=z+6\).
Also, you have four fewer green than blue, or \(y=z-4\).
Thus you have the following system of equations:
\[\begin{cases}x+y+z=50&\text{total number of marbles}\\
x=z+6&\text{number of reds in terms of blues}\\
y=z-4&\text{number of greens in terms of blues}
\end{cases}\]
Your task is to solve for \(z\), the number of blue marbles. Fairly simple, just plug in the given expressions:
\[x+y+z=50~~\iff~~\color{red}{z+6}+\color{green}{z-4}+\color{blue}z=50\]
Solve for \(z\).