Question

A disk comes in a package of 10, with each disk costing 80 cents. By purchasing in bulk, the manager can save 25% of the cost. How many boxes of disks did the manager buy if the disks were purchased in bulk and the total cost was $1447?

A) 20 boxes

B) 25 boxes

C) 15 boxes

D) 30 boxes

E) 35 boxes

Answer 1

The disks were purchased in bulk and the total cost was $1447

D) 30 boxes**

Step-by-step explanation:

The total cost for the disks can be calculated by multiplying the number of boxes by the cost per box. If each box contains 10 disks, the total number of disks is 10 times the number of boxes. Let's denote the number of boxes as x. The cost per box is given as 80 cents, which is equal to $0.80. Therefore, the total cost
`(\(C\))` can be expressed as:

`\[ C = 0.80 * 10 * x \]`

Since the manager can save 25% of the cost by purchasing in bulk, the discounted cost
`(\(D\))` is given by:

`\[ D = C - 0.25 * C \]`

The problem states that the total cost was $1447. So, we can set up the equation:

`\[ D = 1447 \]`

Substituting the expressions for
`\(C\) and \(D\)`, we get:

`\[ 1447 = (0.80 * 10 * x) - 0.25 * (0.80 * 10 * x) \]`

Now, solve for x to find the number of boxes:

`\[ 1447 = 0.75 * (0.80 * 10 * x) \]`

`\[ x = (1447)/(0.75 * 0.80 * 10) \]`

Calculating this value gives
`\(x \approx 30\).` Therefore, the manager bought 30 boxes of disks, and the correct answer is D) 30 boxes.