Question

4 thumb drives and 1 compact disk have a total capacity of 18 gigabytes. 3 compact disks and 4 thumb drives have a total capacity of 22 gigabytes. find the capacity of 1 thumb drive (x) and the capacity of 1 compact disk (y). solution ( capacity of a thumb drive? capacity of a compact disk? )

Explanation:

Step1: Define variables & equations

Let $x$ = thumb drive capacity, $y$ = compact disk capacity.

$$\begin{cases} 4x + y = 18 \\ 3y + 4x = 22 \end{cases}$$

Step2: Subtract first equation from second

Eliminate $4x$ to solve for $y$.
$$(3y + 4x) - (4x + y) = 22 - 18$$
$$2y = 4$$
$$y = 2$$

Step3: Substitute $y=2$ into first equation

Solve for $x$.
$$4x + 2 = 18$$
$$4x = 16$$
$$x = 4$$

Answer:

Capacity of a thumb drive? 4 gb
Capacity of a compact disk? 2 gb