Question

7
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 ( , )

Explanation:

Step1: Define equations from given data

Let $x$ = thumb drive capacity, $y$ = compact disk capacity.
Equation 1: $4x + y = 18$
Equation 2: $3y + 4x = 22$

Step2: Eliminate $4x$ via subtraction

Subtract Equation 1 from Equation 2:
$$(3y + 4x) - (4x + y) = 22 - 18$$
$$2y = 4$$

Step3: Solve for $y$

Divide both sides by 2:
$$y = \frac{4}{2} = 2$$

Step4: Substitute $y$ into Equation 1

$$4x + 2 = 18$$
$$4x = 18 - 2 = 16$$

Step5: Solve for $x$

Divide both sides by 4:
$$x = \frac{16}{4} = 4$$

Answer:

Capacity of 1 thumb drive: 4 gigabytes, Capacity of 1 compact disk: 2 gigabytes