To determine if a customer can buy pool accessories within a given budget after tax, solve a system of equations to find the costs of each item and calculate the total cost including tax.
To determine if a customer who has $200 can buy 1 chlorine filter, 1 raft, and 1 large lounge chair after a sales tax of 5.75% is applied, we need to find the total cost of the items including tax and compare it to the available budget. Let x = cost of 1 raft, y = cost of 1 chlorine filter, and z = cost of 1 large lounge chair. From the given equations:
x + 2y = 220
y + 2z = 245
x + 4z = 315
We can solve this system of equations to find the values of x, y, and z. Once we have those values, we can calculate the total cost including tax by adding the prices of each item and multiplying by 1 + the tax rate. Finally, we compare the total cost to the available budget of $200 to determine if the purchase is affordable.