A souvenir store charges PHP 15.00 per keychain for the first 50 orders. If the order exceeds to 50 keychains, the store charges PHP 12.50 per keychains for the exceeded orders of keychains. Express the total cost K(x) of the x number of keychains as a function of x.
For the first 50 keychains, the cost is PHP 15.00 per keychain. So, the cost for the first 50 keychains is 15*x, where x is the number of keychains.
If the order exceeds 50 keychains, the store charges PHP 12.50 per keychain for the exceeded orders. So, the cost for the exceeded orders is 12.50*(x-50).
Thus, the total cost K(x) of the x number of keychains is given by:
K(x) = 15*x + 12.50*(x-50)
Simplifying further:
K(x) = 15x + 12.50x - 12.50*50
K(x) = 27.50x - 625
To express the total cost K(x) of x number of keychains as a function of x, we can use the following steps:
1. Determine the cost for the first 50 keychains:
- The store charges PHP 15.00 per keychain for the first 50 orders.
- Therefore, the cost for the first 50 keychains would be 50 * PHP 15.00 = PHP 750.00.
2. Determine the cost for the exceeded orders:
- If the order exceeds 50 keychains, the store charges PHP 12.50 per keychain for the exceeded orders.
- Therefore, for each exceeded keychain, the cost would be PHP 12.50.
- So, the cost for the exceeded orders would be (x - 50) * PHP 12.50.
3. Calculate the total cost K(x):
- The total cost K(x) of x number of keychains can be expressed as follows:
K(x) = Cost for the first 50 keychains + Cost for the exceeded orders
K(x) = PHP 750.00 + (x - 50) * PHP 12.50
Therefore, the total cost K(x) of x number of keychains can be expressed as the function K(x) = PHP 750.00 + (x - 50) * PHP 12.50.