Question

A supermarket announced a promotion: if you buy 5 units for $k each, then every additional unit will cost you $m less. Which expression represents the costs of n units, if n > 5?

a) (5n + (n-5)m)
b) (5k + nm)
c) (nk - 5m)
d) (5k + (n-5)(k-m))

Answer 1

The correct expression representing the cost of n units, where n is greater than 5 and there is a discount m on units after the fifth, is 5k + (n - 5)(k - m), reflecting both the full price for the first 5 units and the discounted price for additional units.

Step-by-step explanation:

The question is asking to find the expression that represents the cost of n units at a supermarket, given that the first 5 units are priced at k dollars each, and every additional unit beyond 5 units costs m dollars less. Since we know that the customer will pay full price for the first 5 units and a discounted price for any units beyond that, we must construct an expression that accounts for both the full price and the discounted price.

For the first 5 units, the cost is 5 times the price per unit, so the expression begins with 5k. For every unit beyond 5, the cost is the regular price k minus the discount m, giving us the expression (k - m) for the cost of each additional unit. Since we are calculating the cost for n units (where n is greater than 5), we need to calculate the cost for n - 5 additional units. This part of the expression is (n - 5)(k - m). Hence, the total cost for n units is the sum of the cost for 5 units at full price and the cost for the additional units at the discounted price, represented as 5k + (n - 5)(k - m).