Inequalities

Question

a warehouse store sells food and other consumer goods for discounted prices. on average, customers pay 20% less at the warehouse store than they would at other retailers. customers of the warehouse store must pay a $65 membership fee each year. shopping at the warehouse store saves customers money if they purchase x dollars worth of goods per year. which inequality can be used to find the possible values of x?

 

choices are:

x< 0.2x + 65

 

x > 0.2x +65

 

x > 0.8x +65

 

x > 0.8x - 65

 

Answer 1

Let's find an expression for how much a customer at the warehouse will pay each year. They'll pay a flat fee of $65 plus whatever they paid for the goods. Since they save 20% on all purchases, they only wind up spending 80% of the goods' values. That means, for goods, they pay 0.8x. So warehouse customers spend 0.8x + 65 every year.

 

If warehouse customers weren't shopping there, they would have paid no membership fee, but they would have paid the full x dollars for goods. So the customers would have spent x every year without the warehouse.

 

For shopping at the warehouse to save customers money, the warehouse cost must be less than the cost customers would have spent without the warehouse. Equivalently, the cost customers would have spent without the warehouse must be greater than the warehouse cost.

 

 

We can write that expression like so:

 

x > 0.8x + 65