Question

Write a function to describe the following scenario.

Jonathan is selling his old trading cards.
Each customer that buys gets the first
box they purchase for $10, and each
additional box for only $5.
y = [?]x + [?]

Answer 1

To describe this scenario as a function, we can define "x" as the number of boxes purchased and "y" as the total cost for those boxes. Since the first box costs $10 and each additional box costs $5, we can write the function as:

y = 5(x - 1) + 10

In this function, "x - 1" represents the number of additional boxes purchased after the first box, and multiplying that by $5 gives us the cost of those additional boxes. Adding $10 for the first box gives us the total cost for all the boxes.

Therefore, the function to describe this scenario is:

y = 5(x - 1) + 10

Answer 2

y = 5x + 5

Explanation:

If x is the number of boxes sold and y is the cost

The first box costs $10

Each additional box costs $5.

If the total number of boxes sold is x, then after selling the first box for $10, there will be x - 1 boxes left to be sold

The cost of x -1 boxes at $5 per box = 5(x - 1) = 5x - 5

Therefore for a total of x boxes sold the total cost, y in dollars is
y = 10 (for the first box) + 5x - 5 (for the remaining x - 1 boxes)

= 10 + 5x - 5

= 5 + 5x

which in standard form is written as
y = 5x + 5

We can verify our equation using specific numbers for x
For x = 1
y = 5 + 5(1) = 10 ; since only one box has been sold, the cost is fixed at $10

For x = 2 y = 5 + 5(2) = 5 + 10 = $15
This works out to since first box is sold at $10 and the second box at $5

Leave it to you to work out for other numbers